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  Subjects -> MATHEMATICS (Total: 864 journals)
    - APPLIED MATHEMATICS (68 journals)
    - GEOMETRY AND TOPOLOGY (19 journals)
    - MATHEMATICS (643 journals)
    - MATHEMATICS (GENERAL) (40 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (75 journals)

MATHEMATICS (643 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 20)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 10)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 4)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 15)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access  
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Analysis & Computational Mathematics     Hybrid Journal   (Followers: 5)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 1)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 5)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Journal Cover Communications On Pure & Applied Mathematics
  [SJR: 4.177]   [H-I: 74]   [3 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0010-3640 - ISSN (Online) 1097-0312
   Published by John Wiley and Sons Homepage  [1616 journals]
  • Large Deviations for Stationary Measures of Stochastic Nonlinear Wave
           Equations with Smooth White Noise
    • Authors: Davit Martirosyan
      Abstract: The paper is devoted to the derivation of the large deviations principle for the family of stationary measures of the Markov process generated by the flow of the damped nonlinear wave equations with vanishing white noise. One of the main novelties here is that we do not assume that the deterministic equation possesses a unique equilibrium and we do not impose roughness on the noise. We introduce a new mathematical tool called the generalized stationary measure, which, informally speaking, is a stationary measure that is not necessarily σ-additive. We show that any Markov operator admits such a measure and use this to develop the Freidlin-Wentzell and Khasminskii approaches to the infinite-dimensional setting. We also extend Sowers' method when establishing exponential tightness. Some ingredients of the proof rely on rather nonstandard techniques.© 2016 Wiley Periodicals, Inc.
      PubDate: 2017-03-17T05:25:45.4721-05:00
      DOI: 10.1002/cpa.21693
       
  • Pointwise Estimates and Regularity in Geometric Optics and Other Generated
           Jacobian Equations
    • Authors: Nestor Guillen; Jun Kitagawa
      Abstract: The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge-Ampère type known as generated Jacobian equations. This class of equations, whose general existence theory has been recently developed by Trudinger, goes beyond the framework of optimal transport. We obtain pointwise estimates for weak solutions of such equations under minimal structural and regularity assumptions, covering situations analogous to those of costs satisfying the A3-weak condition introduced by Ma, Trudinger, and Wang in optimal transport. These estimates are used to develop a C1,α regularity theory for weak solutions of Aleksandrov type. The results are new even for all known near-field reflector/refractor models, including the point source and parallel beam reflectors, and are applicable to problems in other areas of geometry, such as the generalized Minkowski problem. © 2016 Wiley Periodicals, Inc.
      PubDate: 2017-03-11T02:15:25.448477-05:
      DOI: 10.1002/cpa.21691
       
  • Uniqueness of Tangent Cones for Two-Dimensional Almost-Minimizing Currents
    • Authors: Camillo De Lellis; Emanuele Spadaro, Luca Spolaor
      Abstract: We consider two-dimensional integer rectifiable currents that are almost area minimizing and show that their tangent cones are everywhere unique. Our argument unifies a few uniqueness theorems of the same flavor, which are all obtained by a suitable modification of White's original theorem for area-minimizing currents in the euclidean space. This note is also the first step in a regularity program for semicalibrated two-dimensional currents and spherical cross sections of three-dimensional area-minimizing cones.© 2016 Wiley Periodicals, Inc.
      PubDate: 2017-03-01T03:15:44.210435-05:
      DOI: 10.1002/cpa.21690
       
  • Riemann-Hilbert Problems for the Shapes Formed by Bodies Dissolving,
           Melting, and Eroding in Fluid Flows
    • Authors: M. Nicholas J. Moore
      Abstract: The classical Stefan problem involves the motion of boundaries during phase transition, but this process can be greatly complicated by the presence of a fluid flow. Here we consider a body undergoing material loss due to either dissolution (from molecular diffusion), melting (from thermodynamic phase change), or erosion (from fluid-mechanical stresses) in a fast-flowing fluid. In each case, the task of finding the shape formed by the shrinking body can be posed as a singular Riemann-Hilbert problem. A class of exact solutions captures the rounded surfaces formed during dissolution/melting, as well as the angular features formed during erosion, thus unifying these different physical processes under a common framework. This study, which merges boundary-layer theory, separated-flow theory, and Riemann-Hilbert analysis, represents a rare instance of an exactly solvable model for high-speed fluid flows with free boundaries.© 2017 Wiley Periodicals, Inc.
      PubDate: 2017-03-01T03:10:34.407137-05:
      DOI: 10.1002/cpa.21689
       
  • Compactness of Alexandrov-Nirenberg Surfaces
    • Authors: Qing Han; Jiaxing Hong, Genggeng Huang
      Abstract: We study a class of compact surfaces in ℝ3 introduced by Alexandrov and generalized by Nirenberg and prove a compactness result under suitable assumptions on induced metrics and Gauss curvatures. © 2016 Wiley Periodicals, Inc.
      PubDate: 2017-02-16T02:00:34.949701-05:
      DOI: 10.1002/cpa.21686
       
  • Arithmetic Spectral Transitions for the Maryland Model
    • Authors: Svetlana Jitomirskaya; Wencai Liu
      Abstract: We give a precise description of spectra of the Maryland model(hλ,α,θu)n=un+1+un−1+λtanπ(θ+nα)un for all values of parameters. We introduce an arithmetically defined index δ(α,θ) and show that for α∉ℚ,σsc(hλ,α,θ)={e:γλ(e)
      PubDate: 2017-02-16T01:40:24.978002-05:
      DOI: 10.1002/cpa.21688
       
  • Spectral Approach to D-bar Problems
    • Authors: Christian Klein; Kenneth D. T-R McLaughlin
      Abstract: We present the first numerical approach to D-bar problems having spectral convergence for real analytic, rapidly decreasing potentials. The proposed method starts from a formulation of the problem in terms of an integral equation that is numerically solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system that is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is considered. The result is used to test direct numerical solutions of the PDE.© 2016 Wiley Periodicals, Inc.
      PubDate: 2017-02-16T01:35:27.991023-05:
      DOI: 10.1002/cpa.21684
       
  • Mutual Absolute Continuity of Interior and Exterior Harmonic Measure
           Implies Rectifiability
    • Authors: Jonas Azzam; Mihalis Mourgoglou, Xavier Tolsa
      Abstract: We show that, for disjoint domains in the euclidean space whose boundaries satisfy a nondegeneracy condition, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rectifiability in the intersection of their boundaries. © 2016 Wiley Periodicals, Inc.
      PubDate: 2017-02-15T01:16:04.044808-05:
      DOI: 10.1002/cpa.21687
       
  • Mean-Field Interaction of Brownian Occupation Measures II: A Rigorous
           Construction of the Pekar Process
    • Authors: Erwin Bolthausen; Wolfgang König, Chiranjib Mukherjee
      Abstract: We consider mean-field interactions corresponding to Gibbs measures on interacting Brownian paths in three dimensions. The interaction is self-attractive and is given by a singular Coulomb potential. The logarithmic asymptotics of the partition function for this model were identified in the 1980s by Donsker and Varadhan in terms of the Pekar variational formula, which coincides with the behavior of the partition function of the polaron problem under strong coupling. Based on this, in 1986 Spohn made a heuristic observation that the strong coupling behavior of the polaron path measure, on certain time scales, should resemble a process, named as the Pekar process, whose distribution could somehow be guessed from the limiting asymptotic behavior of the mean-field measures under interest, whose rigorous analysis remained open. The present paper is devoted to a precise analysis of these mean-field path measures and convergence of the normalized occupation measures towards an explicit mixture of the maximizers of the Pekar variational problem. This leads to a rigorous construction of the aforementioned Pekar process and hence is a contribution to the understanding of the “mean-field approximation” of the polaron problem on the level of path measures.The method of our proof is based on the compact large deviation theory developed by Mukherjee and Varadhan in 2016; its extension to the uniform strong metric for the singular Coulomb interaction was carried out by König and Mukherjee in 2015, as well as an idea inspired by a partial path exchange argument appearing in 1997 in work by Bolthausen and Schmock. © 2016 Wiley Periodicals, Inc.
      PubDate: 2017-01-11T06:10:20.055249-05:
      DOI: 10.1002/cpa.21682
       
  • Characterization of Metal Artifacts in X-Ray Computed Tomography
    • Authors: Hyoung Suk Park; Jae Kyu Choi, Jin Keun Seo
      Abstract: Metal streak artifacts in X-ray computerized tomography (CT) are characterized here using the notion of the wavefront set from microlocal analysis. The metal artifacts are caused mainly from the mismatch of the forward model of the filtered back-projection; the presence of metallic subjects in an imaging subject violates the model's assumption of the CT sinogram data being the Radon transform of an image. The increasing use of metallic implants has increased demand for the reduction of metal artifacts in the field of dental and medical radiography. However, it is a challenging issue due to the serious difficulties in analyzing the X-ray data, which depends nonlinearly on the distribution of the metallic subject. In this paper, we, for the first time, provide a mathematical analysis to characterize the structure of metal streaking artifacts. The metal streaking artifacts are produced along the line tangent to boundaries of the metal region touching at least two different boundaries. We also found a sufficient condition for the nonexistence of the metal streaking artifacts.© 2016 Wiley Periodicals, Inc.
      PubDate: 2017-01-04T07:25:36.23014-05:0
      DOI: 10.1002/cpa.21680
       
  • Issue Information – TOC
    • Pages: 813 - 813
      PubDate: 2017-03-17T05:26:27.830603-05:
      DOI: 10.1002/cpa.21660
       
  • Corrigendum: Viscosity Solutions to Complex Monge-Ampère Equations
    • Authors: Philippe Eyssidieux; Vincent Guedj, Ahmed Zeriahi
      Pages: 815 - 821
      Abstract: The proof of the comparison principle in the article cited above is not complete. We provide here an alternative proof, valid in the ample locus of any big cohomology class, and discuss the resulting modifications.© 2017 Wiley Periodicals, Inc.
      PubDate: 2017-03-17T05:26:27.658791-05:
      DOI: 10.1002/cpa.21692
       
  • Gluing Eguchi-Hanson Metrics and a Question of Page
    • Authors: Simon Brendle; Nikolaos Kapouleas
      Abstract: In 1978, Gibbons-Pope and Page proposed a physical picture for the Ricci flat Kähler metrics on the K3 surface based on a gluing construction. In this construction, one starts from a flat torus with 16 orbifold points and resolves the orbifold singularities by gluing in 16 small Eguchi-Hanson manifolds that all have the same orientation. This construction was carried out rigorously by Topiwala, LeBrun-Singer, and Donaldson.In 1981, Page asked whether the above construction can be modified by reversing the orientations of some of the Eguchi-Hanson manifolds. This is a subtle question: if successful, this construction would produce Einstein metrics that are neither Kähler nor self-dual.In this paper, we focus on a configuration of maximal symmetry involving eight small Eguchi-Hanson manifolds of each orientation that are arranged according to a chessboard pattern. By analyzing the interactions between Eguchi-Hanson manifolds with opposite orientation, we identify a nonvanishing obstruction to the gluing problem, thereby destroying any hope of producing a metric of zero Ricci curvature in this way. Using this obstruction, we are able to understand the dynamics of such metrics under Ricci flow as long as the Eguchi-Hanson manifolds remain small. In particular, for the configuration described above, we obtain an ancient solution to the Ricci flow with the property that the maximum of the Riemann curvature tensor blows up at a rate of (−t)1/2, while the maximum of the Ricci curvature converges to 0. © 2016 Wiley Periodicals, Inc.
      PubDate: 2016-12-22T06:10:22.425571-05:
      DOI: 10.1002/cpa.21678
       
  • Long Time Stability for Solutions of a β-Plane Equation
    • Authors: Tarek M. Elgindi; Klaus Widmayer
      Abstract: We prove stability for arbitrarily long times of the zero solution for the so-called β-plane equation, which describes the motion of a two-dimensional inviscid, ideal fluid under the influence of the Coriolis effect. The Coriolis force introduces a linear dispersive operator into the two-dimensional incompressible Euler equations, thus making this problem amenable to an analysis from the point of view of nonlinear dispersive equations. The dispersive operator, L1 ≔ ∂1/ ∇ 2, exhibits good decay, but has numerous unfavorable properties, chief among which are its anisotropy and its behavior at small frequencies.© 2016 Wiley Periodicals, Inc.
      PubDate: 2016-11-15T01:51:39.011201-05:
      DOI: 10.1002/cpa.21676
       
  • Local Regularity for the Modified SQG Patch Equation
    • Authors: Alexander Kiselev; Yao Yao, Andrej Zlatoš
      Abstract: We study the patch dynamics on the whole plane and on the half-plane for a family of active scalars called modified surface quasi-geostrophic (SQG) equations. These involve a parameter α that appears in the power of the kernel in their Biot-Savart laws and describes the degree of regularity of the equation. The values α=0 and α=½ correspond to the two-dimensional Euler and SQG equations, respectively. We establish here local-in-time regularity for these models, for all α ∊ (0,½) on the whole plane and for all small α > 0 on the half-plane. We use the latter result in [16], where we show existence of regular initial data on the half-plane that lead to a finite-time singularity.© 2016 Wiley Periodicals, Inc.
      PubDate: 2016-11-11T08:35:22.499299-05:
      DOI: 10.1002/cpa.21677
       
  • Stochastic Homogenization of Nonconvex Hamilton-Jacobi Equations: A
           Counterexample
    • Authors: Bruno Ziliotto
      Abstract: This paper provides a counterexample to Hamilton-Jacobi homogenization in the nonconvex case for general stationary ergodic environments.© 2016 Wiley Periodicals, Inc.
      PubDate: 2016-10-25T09:20:23.951907-05:
      DOI: 10.1002/cpa.21674
       
  • Linear Inviscid Damping for a Class of Monotone Shear Flow in Sobolev
           Spaces
    • Authors: Dongyi Wei; Zhifei Zhang, Weiren Zhao
      Abstract: In this paper, we prove the decay estimates of the velocity and H1 scattering for the two-dimensional linearized Euler equations around a class of monotone shear flow in a finite channel. Our result is consistent with the decay rate predicted by Case in 1960.© 2016 Wiley Periodicals, Inc.
      PubDate: 2016-10-24T01:10:26.513651-05:
      DOI: 10.1002/cpa.21672
       
  • Infinite Speed of Propagation and Regularity of Solutions to the
           Fractional Porous Medium Equation in General Domains
    • Authors: Matteo Bonforte; Alessio Figalli, Xavier Ros-Oton
      Abstract: We study the positivity and regularity of solutions to the fractional porous me\-dium equations ut + (−Δ)sum=0 in (0,∞) × Ω for m > 1 and s ∊ (0,1), with Dirichlet boundary data u=0 in (0,∞) × (ℝN∖Ω) and nonnegative initial condition u(0,·,)=u0 ≥ 0.Our first result is a quantitative lower bound for solutions that holds for all positive times t > 0. As a consequence, we find a global Harnack principle stating that for any t > 0 solutions are comparable to ds/m, where d is the distance to ∂Ω. This is in sharp contrast with the local case s=1, where the equation has finite speed of propagation.After this, we study the regularity of solutions. We prove that solutions are classical in the interior (C∞ in x and C1,α in t) and establish a sharp Cxs/m regularity estimate up to the boundary.Our methods are quite general and can be applied to wider classes of nonlocal parabolic equations of the form ut + ℒF(u) = 0 in Ω, both in bounded and unbounded domains.© 2016 Wiley Periodicals, Inc.
      PubDate: 2016-10-19T05:20:21.903843-05:
      DOI: 10.1002/cpa.21673
       
  • On the Two-Dimensional Muskat Problem with Monotone Large Initial Data
    • Authors: Fan Deng; Zhen Lei, Fanghua Lin
      Abstract: We consider the evolution of two incompressible, immiscible fluids with different densities in porous media, known as the Muskat problem [21], which in two dimensions is analogous to the Hele-Shaw cell [24]. We establish, for a class of large and monotone initial data, the global existence of weak solutions. The proof is based on a local well-posedness result for the initial data with certain specific asymptotics at spatial infinity and a new maximum principle for the first derivative of the graph function. © 2016 Wiley Periodicals, Inc.
      PubDate: 2016-09-20T05:30:22.890244-05:
      DOI: 10.1002/cpa.21669
       
  • Existence and Uniqueness for a Crystalline Mean Curvature Flow
    • Authors: Antonin Chambolle; Massimiliano Morini, Marcello Ponsiglione
      Abstract: An existence and uniqueness result, up to fattening, for a class of crystalline mean curvature flows with natural mobility is proved. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets. The comparison principle is obtained by means of a suitable weak formulation of the flow, while the existence of a global-in-time solution follows via a minimizing movement approach.© 2016 Wiley Periodicals, Inc.
      PubDate: 2016-09-01T08:15:20.874762-05:
      DOI: 10.1002/cpa.21668
       
  • Boundary Value Problems for Second-Order Elliptic Operators Satisfying a
           Carleson Condition
    • Authors: Martin Dindoš; Jill Pipher, David Rule
      Abstract: Let Ω be a Lipschitz domain in ℝn, n ≥ 2, and L = div A∇· be a second-order elliptic operator in divergence form. We establish the solvability of the Dirichlet regularity problem with boundary data in H1,p(∂Ω) and of the Neumann problem with Lp(∂Ω) data for the operator L on Lipschitz domains with small Lipschitz constant. We allow the coefficients of the operator L to be rough, obeying a certain Carleson condition with small norm. These results complete the results of Dindoš, Petermichl, and Pipher (2007), where the Lp(∂Ω) Dirichlet problem was considered under the same assumptions, and Dindoš and Rule (2010), where the regularity and Neumann problems were considered on two-dimensional domains.© 2016 Wiley Periodicals, Inc.
      PubDate: 2016-06-13T09:40:25.675676-05:
      DOI: 10.1002/cpa.21649
       
  • On the Global Solution of a 3-D MHD System with Initial Data near
           Equilibrium
    • Authors: Hammadi Abidi; Ping Zhang
      Abstract: In this paper, we prove the global existence of smooth solutions to the three-dimensional incompressible magnetohydrodynamical system with initial data close enough to the equilibrium state, (e3,0). Compared with previous works by Lin, Xu, and Zhang and by Xu and Zhang, here we present a new Lagrangian formulation of the system, which is a damped wave equation and which is nondegenerate only in the direction of the initial magnetic field. Furthermore, we remove the admissible condition on the initial magnetic field, which was required in the earlier works. By using the Frobenius theorem and anisotropic Littlewood-Paley theory for the Lagrangian formulation of the system, we achieve the global L1-in-time Lipschitz estimate of the velocity field, which allows us to conclude the global existence of solutions to this system. In the case when the initial magnetic field is a constant vector, the large-time decay rate of the solution is also obtained.© 2016 Wiley Periodicals, Inc.
      PubDate: 2016-05-10T03:20:22.857425-05:
      DOI: 10.1002/cpa.21645
       
  • Long-Time Behavior, Invariant Measures, and Regularizing Effects for
           Stochastic Scalar Conservation Laws
    • Authors: Benjamin Gess; Panagiotis E. Souganidis
      Abstract: We study the long-time behavior and regularity of the pathwise entropy solutions to stochastic scalar conservation laws with random-in-time spatially homogeneous fluxes and periodic initial data. We prove that the solutions converge to their spatial average, which is the unique invariant measure of the associated random dynamical system, and provide a rate of convergence, the latt3er being new even in the deterministic case for dimensions higher than 2. The main tool is a new regularization result in the spirit of averaging lemmata for scalar conservation laws, which, in particular, implies a regularization by noise-type result for pathwise quasi-solutions.© 2016 Wiley Periodicals, Inc.
      PubDate: 2016-05-10T03:20:22.063664-05:
      DOI: 10.1002/cpa.21646
       
  • Singularities of Solutions to Quadratic Vector Equations on the Complex
           Upper Half-Plane
    • Authors: O. Ajanki; L. Erdős, T. Krüger
      Abstract: Let S be a positivity-preserving symmetric linear operator acting on bounded functions. The nonlinear equation −1m=z+Sm with a parameter z in the complex upper half-plane ℍ has a unique solution m with values in ℍ. We show that the z-dependence of this solution can be represented as the Stieltjes transforms of a family of probability measures v on ℝ. Under suitable conditions on S, we show that v has a real analytic density apart from finitely many algebraic singularities of degree at most 3.Our motivation comes from large random matrices. The solution m determines the density of eigenvalues of two prominent matrix ensembles: (i) matrices with centered independent entries whose variances are given by S and (ii) matrices with correlated entries with a translation-invariant correlation structure. Our analysis shows that the limiting eigenvalue density has only square root singularities or cubic root cusps; no other singularities occur.© 2016 Wiley Periodicals, Inc.
      PubDate: 2016-04-09T05:31:04.786506-05:
      DOI: 10.1002/cpa.21639
       
  • Well-Posed Treatment of Space-Charge Layers in the Electroneutral Limit of
           Electrodiffusion
    • Authors: Adam R. Stinchcombe; Yoichiro Mori, Charles S. Peskin
      Abstract: The electroneutral model describes cellular electrical activity, accounting for ionic concentration dynamics without resolution of the fine spatial scales of the space-charge layer. This is done by asserting that the ionic solution is electrically neutral at each point in space. However, electroneutrality is inconsistent with the original boundary conditions at cell membranes. We consider three separate methods of resolving this inconsistency that result in well-posed models that are accurate approximations to a detailed model in which the space-charge layer is fully resolved. A particular electrodiffusion problem is utilized to make the discussion specific. © 2016 Wiley Periodicals, Inc.
      PubDate: 2016-02-29T05:36:40.978415-05:
      DOI: 10.1002/cpa.21630
       
  • Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving
           Linear Systems
    • Authors: Yuxin Chen; Emmanuel J. Candès
      Pages: 822 - 883
      Abstract: We consider the fundamental problem of solving quadratic systems of equations in yi= 〈ai,x〉 2, i=1,…,m, and x∈ℝn is unknown. We propose a novel method, which starts with an initial guess computed by means of a spectral method and proceeds by minimizing a nonconvex functional as in the Wirtinger flow approach [13]. There are several key distinguishing features, most notably a distinct objective functional and novel update rules, which operate in an adaptive fashion and drop terms bearing too much influence on the search direction. These careful selection rules provide a tighter initial guess, better descent directions, and thus enhanced practical performance. On the theoretical side, we prove that for certain unstructured models of quadratic systems, our algorithms return the correct solution in linear time, i.e., in time proportional to reading the data {ai} and {yi} as soon as the ratio m/n between the number of equations and unknowns exceeds a fixed numerical constant. We extend the theory to deal with noisy systems in which we only have yi≈ 〈ai,x〉 2 and prove that our algorithms achieve a statistical accuracy, which is nearly unimprovable. We complement our theoretical study with numerical examples showing that solving random quadratic systems is both computationally and statistically not much harder than solving linear systems of the same size—hence the title of this paper. For instance, we demonstrate empirically that the computational cost of our algorithm is about four times that of solving a least squares problem of the same size. © 2016 Wiley Periodicals, Inc.
      PubDate: 2016-04-06T04:23:52.432964-05:
      DOI: 10.1002/cpa.21638
       
  • Propagation of Reactions in Inhomogeneous Media
    • Authors: Andrej Zlatoš
      Pages: 884 - 949
      Abstract: Consider reaction-diffusion equation ut=Δ u + f(x,u) with x∈ℝd and general inhomogeneous ignition reaction f ≥ 0 vanishing at u = 0,1. Typical solutions 0 ≤ u ≤ 1 transition from 0 to 1 as time progresses, and we study them in the region where this transition occurs. Under fairly general qualitative hypotheses on f we show that in dimensions d ≤ 3, the Hausdorff distance of the superlevel sets {u ≥ ε } and {u ≥ 1-ε} remains uniformly bounded in time for each ε ∊ (0,1). Thus, u remains uniformly in time close to the characteristic function of { u≥12 } in the sense of Hausdorff distance of superlevel sets. We also show that each {u ≥ ε} expands with average speed (over any long enough time interval) between the two spreading speeds corresponding to any x-independent lower and upper bounds on f. On the other hand, these results turn out to be false in dimensions d ≥ 4, at least without further quantitative hypotheses on f. The proof for d ≤ 3 is based on showing that as the solution propagates, small values of u cannot escape far ahead of values close to 1. The proof for d ≥ 4 is via construction of a counterexample for which this fails. Such results were before known for d=1 but are new for general non-periodic media in dimensions d ≥ 2 (some are also new for homogeneous and periodic media). They extend in a somewhat weaker sense to monostable, bistable, and mixed reaction types, as well as to transitions between general equilibria u−≤u+ of the PDE and to solutions not necessarily satisfying u−≤u≤u+. © 2016 Wiley Periodicals, Inc.
      PubDate: 2016-07-13T01:25:24.541977-05:
      DOI: 10.1002/cpa.21653
       
  • Further Time Regularity for Nonlocal, Fully Nonlinear Parabolic Equations
    • Authors: Héctor A. Chang-Lara; Dennis Kriventsov
      Pages: 950 - 977
      Abstract: We establish Hölder estimates for the time derivative of solutions of nonlocal parabolic equations under mild assumptions for the boundary data. As a consequence we are able to extend the Evans-Krylov estimate for rough kernels to parabolic equations. © 2016 Wiley Periodicals, Inc.
      PubDate: 2016-10-03T02:06:27.857452-05:
      DOI: 10.1002/cpa.21671
       
  • Coarsening of Folds in Hanging Drapes
    • Authors: Peter Bella; Robert V. Kohn
      Pages: 978 - 1021
      Abstract: We consider the elastic energy of a hanging drape—a thin elastic sheet, pulled down by the force of gravity, with fine-scale folding at the top that achieves approximately uniform confinement. This example of energy-driven pattern formation in a thin elastic sheet is of particular interest because the length scale of folding varies with height. We focus on how the minimum elastic energy depends on the physical parameters. As the sheet thickness vanishes, the limiting energy is due to the gravitational force and is relatively easy to understand. Our main accomplishment is to identify the “scaling law” of the correction due to positive thickness. We do this by (i) proving an upper bound, by considering the energies of several constructions and taking the best; and (ii) proving an ansatz-free lower bound, which agrees with the upper bound up to a parameter-independent prefactor. The coarsening of folds in hanging drapes has also been considered in the recent physics literature, by using a self-similar construction whose basic cell has been called a “wrinklon.” Our results complement and extend that work by showing that self-similar coarsening achieves the optimal scaling law in a certain parameter regime, and by showing that other constructions (involving lateral spreading of the sheet) do better in other regions of parameter space. Our analysis uses a geometrically linear Föppl-von Kármán model for the elastic energy, and is restricted to the case when Poisson's ratio is 0. © 2016 Wiley Periodicals, Inc.
      PubDate: 2016-05-04T08:25:42.082638-05:
      DOI: 10.1002/cpa.21643
       
 
 
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