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  Subjects -> MATHEMATICS (Total: 889 journals)
    - APPLIED MATHEMATICS (73 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (659 journals)
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MATHEMATICS (659 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
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: 25)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
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: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 8)
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: 5)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
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: 6)
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: 9)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
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: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
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: 3)
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: 11)
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: 7)
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 Network Science     Open Access   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
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: 20)
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: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
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: 5)
BIBECHANA     Open Access   (Followers: 1)
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: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 9)
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: 1)
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: 20)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (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: 3)
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: 14)
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: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
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: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
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)

        1 2 3 4 | Last

Journal Cover Calculus of Variations and Partial Differential Equations
  [SJR: 2.455]   [H-I: 44]   [0 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1432-0835 - ISSN (Online) 0944-2669
   Published by Springer-Verlag Homepage  [2352 journals]
  • A new and extended variational characterization of the Fučík Spectrum
           with application to nonresonance and resonance problems
    • Authors: Pavel Drábek; Stephen B. Robinson
      Abstract: We consider the boundary value problem $$\begin{aligned} -\Delta u= & {} \alpha u^{+}-\beta u^{-} \quad \hbox { in } \Omega ,\\ u= & {} 0 \quad \hbox { on }\partial \Omega , \end{aligned}$$ where \(\Omega \) is a smooth bounded domain in \({\mathbb {R}}^N,u^{\pm }:=\max \{\pm \,u,0\}\) , and \((\alpha ,\beta )\in {\mathbb {R}}^2\) . When this problem has a nontrivial solution, then \((\alpha ,\beta )\) is an element of the Fučík Spectrum, \(\Sigma \) . Our main result is to extend the variational characterization, due to Castro and Chang in 2010, of several curves in \(\Sigma \) . As an application we prove existence theorems for nonresonance and resonance problems relative to these extended spectral curves.
      PubDate: 2017-11-10
      DOI: 10.1007/s00526-017-1276-8
      Issue No: Vol. 57, No. 1 (2017)
       
  • On the 4D nonlinear Schrödinger equation with combined terms under
           the energy threshold
    • Authors: Changxing Miao; Tengfei Zhao; Jiqiang Zheng
      Abstract: In this paper, we consider the longtime dynamics of the solutions to focusing energy-critical Schrödinger equation with a defocusing energy-subcritical perturbation term under a ground state energy threshold in four spatial dimension. This extends the results in Miao et al. (Commun Math Phys 318(3):767–808, 2013, The dynamics of the NLS with the combined terms in five and higher dimensions. Some topics in harmonic analysis and applications, advanced lectures in mathematics, ALM34, Higher Education Press, Beijing, pp 265–298, 2015) to four dimension without radial assumption and the proof of scattering is based on the interaction Morawetz estimates developed in Dodson (Global well-posedness and scattering for the focusing, energy-critical nonlinear Schrödinger problem in dimension \(d =4\) for initial data below a ground state threshold, arXiv:1409.1950), the main ingredients of which requires us to overcome the logarithmic failure in the double Duhamel argument in four dimensions.
      PubDate: 2017-11-09
      DOI: 10.1007/s00526-017-1264-z
      Issue No: Vol. 56, No. 6 (2017)
       
  • First eigenvalue estimates of Dirichlet-to-Neumann operators on graphs
    • Authors: Bobo Hua; Yan Huang; Zuoqin Wang
      Abstract: Following Escobar (J Funct Anal 150(2):544–556, 1997) and Jammes (Ann l’Inst Fourier 65(3):1381–1385, 2015), we introduce two types of isoperimetric constants and give lower bound estimates for the first nontrivial eigenvalues of Dirichlet-to-Neumann operators on finite graphs with boundary respectively.
      PubDate: 2017-11-09
      DOI: 10.1007/s00526-017-1260-3
      Issue No: Vol. 56, No. 6 (2017)
       
  • Index and topology of minimal hypersurfaces in $$\mathbb {R}^n$$ R n
    • Authors: Chao Li
      Abstract: In this paper, we consider immersed two-sided minimal hypersurfaces in \(\mathbb {R}^n\) with finite total curvature. We prove that the sum of the Morse index and the nullity of the Jacobi operator is bounded from below by a linear function of the number of ends and the first Betti number of the hypersurface. When \(n=4\) , we are able to drop the nullity term by a careful study for the rigidity case. Our result is the first effective Morse index bound by purely topological invariants, and is a generalization of Li and Wang (Math Res Lett 9(1):95–104, 2002). Using our index estimates and ideas from the recent work of Chodosh–Ketover–Maximo (Minimal surfaces with bounded index, 2015. arXiv:1509.06724), we prove compactness and finiteness results of minimal hypersurfaces in \(\mathbb {R}^4\) with finite index.
      PubDate: 2017-11-09
      DOI: 10.1007/s00526-017-1272-z
      Issue No: Vol. 56, No. 6 (2017)
       
  • Rigidity and curvature estimates for graphical self-shrinkers
    • Authors: Qiang Guang; Jonathan J. Zhu
      Abstract: Self-shrinkers are hypersurfaces that shrink homothetically under mean curvature flow; these solitons model the singularities of the flow. It is presently known that an entire self-shrinking graph must be a hyperplane. In this paper we show that the hyperplane is rigid in an even stronger sense, namely: for \(2\le n \le 6\) , any smooth, complete self-shrinker \(\Sigma ^n\subset \mathbf {R}^{n+1}\) that is graphical inside a large, but compact, set must be a hyperplane. In fact, this rigidity holds within a larger class of almost stable self-shrinkers. A key component of this paper is the procurement of linear curvature estimates for almost stable shrinkers, and it is this step that is responsible for the restriction on n. Our methods also yield uniform curvature bounds for translating solitons of the mean curvature flow.
      PubDate: 2017-11-08
      DOI: 10.1007/s00526-017-1277-7
      Issue No: Vol. 56, No. 6 (2017)
       
  • Weighted Lorentz estimates for parabolic equations with non-standard
           growth on rough domains
    • Authors: The Anh Bui; Xuan Thinh Duong
      Abstract: The main aim of this paper is to prove the Calderón–Zygmund estimates for a general nonlinear parabolic equation of p(x, t)-Laplacian type in the weighted Lorentz spaces. Note that we only require some mild conditions on the nonlinearity of coefficients and the underlying domain. The result for these nonlinear parabolic equations is new even in the particular case when the growth p(x, t) is a constant.
      PubDate: 2017-11-08
      DOI: 10.1007/s00526-017-1273-y
      Issue No: Vol. 56, No. 6 (2017)
       
  • Bubbling analysis for approximate Lorentzian harmonic maps from Riemann
           surfaces
    • Authors: Xiaoli Han; Jürgen Jost; Lei Liu; Liang Zhao
      Abstract: For a sequence of approximate harmonic maps \((u_n,v_n)\) (meaning that they satisfy the harmonic system up to controlled error terms) from a compact Riemann surface with smooth boundary to a standard static Lorentzian manifold with bounded energy, we prove that identities for the Lorentzian energy hold during the blow-up process. In particular, in the special case where the Lorentzian target metric is of the form \(g_N -\beta dt^2\) for some Riemannian metric \(g_N\) and some positive function \(\beta \) on N, we prove that such identities also hold for the positive energy (obtained by changing the sign of the negative part of the Lorentzian energy) and there is no neck between the limit map and the bubbles. As an application, we complete the blow-up picture of singularities for a harmonic map flow into a standard static Lorentzian manifold. We prove that the energy identities of the flow hold at both finite and infinite singular times. Moreover, the no neck property of the flow at infinite singular time is true.
      PubDate: 2017-11-07
      DOI: 10.1007/s00526-017-1271-0
      Issue No: Vol. 56, No. 6 (2017)
       
  • Ricci curvature and orientability
    • Authors: Shouhei Honda
      Abstract: In this paper we define an orientation of a measured Gromov–Hausdorff limit space of Riemannian manifolds with uniform Ricci bounds from below. This is the first observation of orientability for metric measure spaces. Our orientability has two fundamental properties. One of them is the stability with respect to noncollapsed sequences. As a corollary we see that if the cross section of a tangent cone of a noncollapsed limit space of orientable Riemannian manifolds is smooth, then it is also orientable in the ordinary sense, which can be regarded as a new obstruction for a given manifold to be the cross section of a tangent cone. The other one is that there are only two choices for orientations on a limit space. We also discuss relationships between \(L^2\) -convergence of orientations and convergence of currents in metric spaces. In particular for a noncollapsed sequence, we prove a compatibility between the intrinsic flat convergence by Sormani–Wenger, the pointed flat convergence by Lang–Wenger, and the Gromov–Hausdorff convergence, which is a generalization of a recent work by Matveev–Portegies to the noncompact case. Moreover combining this compatibility with the second property of our orientation gives an explicit formula for the limit integral current by using an orientation on a limit space. Finally dualities between de Rham cohomologies on an oriented limit space are proven.
      PubDate: 2017-11-07
      DOI: 10.1007/s00526-017-1258-x
      Issue No: Vol. 56, No. 6 (2017)
       
  • Interior Calderón–Zygmund estimates for solutions to general parabolic
           equations of p -Laplacian type
    • Authors: Truyen Nguyen
      Abstract: We study general parabolic equations of the form \(u_t = \text{ div }\,\mathbf {A}(x,t, u,D u) +\text{ div }\,( \mathbf {F} ^{p-2} \mathbf {F})+ f\) whose principal part depends on the solution itself. The vector field \(\mathbf {A}\) is assumed to have small mean oscillation in x, measurable in t, Lipschitz continuous in u, and its growth in Du is like the p-Laplace operator. We establish interior Calderón–Zygmund estimates for locally bounded weak solutions to the equations when \(p>2n/(n+2)\) . This is achieved by employing a perturbation method together with developing a two-parameter technique and a new compactness argument. We also make crucial use of the intrinsic geometry method by DiBenedetto (Degenerate parabolic equations, Springer, New York, 1993) and the maximal function free approach by Acerbi and Mingione (Duke Math J 136(2):285–320, 2007).
      PubDate: 2017-11-07
      DOI: 10.1007/s00526-017-1265-y
      Issue No: Vol. 56, No. 6 (2017)
       
  • Regularity for elliptic systems of differential forms and applications
    • Authors: Swarnendu Sil
      Abstract: We prove existence and up to the boundary regularity estimates in \(L^{p}\) and Hölder spaces for weak solutions of the linear system $$\begin{aligned} \delta \left( A d\omega \right) + B^{T}d\delta \left( B\omega \right) = \lambda B\omega + f \text { in } \varOmega , \end{aligned}$$ with either \( \nu \wedge \omega \) and \(\nu \wedge \delta \left( B\omega \right) \) or \(\nu \lrcorner B\omega \) and \(\nu \lrcorner \left( A d\omega \right) \) prescribed on \(\partial \varOmega .\) The proofs are in the spirit of ‘Campanato method’ and thus avoid potential theory and do not require a verification of Agmon–Douglis–Nirenberg or Lopatinskiĭ–Shapiro type conditions. Applications to a number of related problems, such as general versions of the time-harmonic Maxwell system, stationary Stokes problem and the ‘div-curl’ systems, are included.
      PubDate: 2017-11-07
      DOI: 10.1007/s00526-017-1269-7
      Issue No: Vol. 56, No. 6 (2017)
       
  • Time-convexity of the entropy in the multiphasic formulation of the
           incompressible Euler equation
    • Authors: Hugo Lavenant
      Abstract: We study the multiphasic formulation of the incompressible Euler equation introduced by Brenier: infinitely many phases evolve according to the compressible Euler equation and are coupled through a global incompressibility constraint. In a convex domain, we are able to prove that the entropy, when averaged over all phases, is a convex function of time, a result that was conjectured by Brenier. The novelty in our approach consists in introducing a time-discretization that allows us to import a flow interchange inequality previously used by Matthes, McCann and Savaré to study first order in time PDE, namely the JKO scheme associated with non-linear parabolic equations.
      PubDate: 2017-11-04
      DOI: 10.1007/s00526-017-1262-1
      Issue No: Vol. 56, No. 6 (2017)
       
  • Standing waves for a coupled nonlinear Hartree equations with nonlocal
           interaction
    • Authors: Jun Wang; Junping Shi
      Abstract: Standing wave solutions of coupled nonlinear Hartree equations with nonlocal interaction are considered. Such systems arises from mathematical models in Bose–Einstein condensates theory and nonlinear optics. The existence and non-existence of positive ground state solutions are proved under optimal conditions on parameters, and various qualitative properties of ground state solutions are shown. The uniqueness of the positive solution or the positive ground state solution are also obtained in some cases.
      PubDate: 2017-11-04
      DOI: 10.1007/s00526-017-1268-8
      Issue No: Vol. 56, No. 6 (2017)
       
  • Short time existence of the heat flow for Dirac-harmonic maps on closed
           manifolds
    • Authors: Johannes Wittmann
      Abstract: The heat flow for Dirac-harmonic maps on Riemannian spin manifolds is a modification of the classical heat flow for harmonic maps by coupling it to a spinor. It was introduced by Chen, Jost, Sun, and Zhu as a tool to get a general existence program for Dirac-harmonic maps. For source manifolds with boundary they obtained short time existence, and the existence of a global weak solution was established by Jost, Liu, and Zhu. We prove short time existence of the heat flow for Dirac-harmonic maps on closed manifolds.
      PubDate: 2017-11-04
      DOI: 10.1007/s00526-017-1270-1
      Issue No: Vol. 56, No. 6 (2017)
       
  • Stable self-similar blowup in the supercritical heat flow of harmonic maps
    • Authors: Paweł Biernat; Roland Donninger; Birgit Schörkhuber
      Abstract: We consider the heat flow of corotational harmonic maps from \(\mathbb {R}^3\) to the three-sphere and prove the nonlinear asymptotic stability of a particular self-similar shrinker that is not known in closed form. Our method provides a novel, systematic, robust, and constructive approach to the stability analysis of self-similar blowup in parabolic evolution equations. In particular, we completely avoid using delicate Lyapunov functionals, monotonicity formulas, indirect arguments, or fragile parabolic structure like the maximum principle. As a matter of fact, our approach reduces the nonlinear stability analysis of self-similar shrinkers to the spectral analysis of the associated self-adjoint linearized operators.
      PubDate: 2017-11-04
      DOI: 10.1007/s00526-017-1256-z
      Issue No: Vol. 56, No. 6 (2017)
       
  • Index theory for heteroclinic orbits of Hamiltonian systems
    • Authors: Xijun Hu; Alessandro Portaluri
      Abstract: Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian systems and the dynamical consequences of this theory are enormous. Although the index theory in the periodic case is well-established, very few results are known in the case of homoclinic orbits of Hamiltonian systems. Moreover, to the authors’ knowledge, no results have been yet proved in the case of heteroclinic and halfclinic (i.e. parametrized by a half-line) orbits. Motivated by the importance played by these motions in understanding several challenging problems in Classical Mechanics, we develop a new index theory and we prove at once a general spectral flow formula for heteroclinic, homoclinic and halfclinic trajectories. Finally we show how this index theory can be used to recover all the (classical) existing results on orbits parametrized by bounded intervals.
      PubDate: 2017-11-04
      DOI: 10.1007/s00526-017-1259-9
      Issue No: Vol. 56, No. 6 (2017)
       
  • Michell trusses in two dimensions as a $$\Gamma $$ Γ -limit of optimal
           design problems in linear elasticity
    • Authors: Heiner Olbermann
      Abstract: We reconsider the minimization of the compliance of a two dimensional elastic body with traction boundary conditions for a given weight. It is well known how to rewrite this optimal design problem as a nonlinear variational problem. We take the limit of vanishing weight by sending a suitable Lagrange multiplier to infinity in the variational formulation. We show that the limit, in the sense of \(\Gamma \) -convergence, is a certain Michell truss problem. This proves a conjecture by Kohn and Allaire.
      PubDate: 2017-11-03
      DOI: 10.1007/s00526-017-1266-x
      Issue No: Vol. 56, No. 6 (2017)
       
  • Multiplicity and bifurcation of positive solutions for nonhomogeneous
           semilinear fractional Laplacian problems
    • Authors: Bingliang Li; Yongqiang Fu
      Abstract: In this paper we consider the following nonhomogeneous semilinear fractional Laplacian problem $$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^s u+u=\lambda (f(x,u)+h(x)) \,\, \text {in}\,\, \mathbb {R}^N,\\ u\in H^s(\mathbb {R}^N), u>0\,\, \text {in}\,\, \mathbb {R}^N, \end{array}\right. } \end{aligned}$$ where \(\lambda >0\) and \(\lim _{ x \rightarrow \infty }f(x,u)=\overline{f}(u)\) uniformly on any compact subset of \([0,\infty )\) . We prove that under suitable conditions on f and h, there exists \(0<\lambda ^*<+\infty \) such that the problem has at least two positive solutions if \(\lambda \in (0,\lambda ^*)\) , a unique positive solution if \(\lambda =\lambda ^*\) , and no solution if \(\lambda >\lambda ^*\) . We also obtain the bifurcation of positive solutions for the problem at \((\lambda ^*,u^*)\) and further analyse the set of positive solutions.
      PubDate: 2017-11-02
      DOI: 10.1007/s00526-017-1257-y
      Issue No: Vol. 56, No. 6 (2017)
       
  • The Cheeger constant of a Jordan domain without necks
    • Authors: Gian Paolo Leonardi; Robin Neumayer; Giorgio Saracco
      Abstract: We show that the maximal Cheeger set of a Jordan domain \(\Omega \) without necks is the union of all balls of radius \(r = h(\Omega )^{-1}\) contained in \(\Omega \) . Here, \(h(\Omega )\) denotes the Cheeger constant of \(\Omega \) , that is, the infimum of the ratio of perimeter over area among subsets of \(\Omega \) , and a Cheeger set is a set attaining the infimum. The radius r is shown to be the unique number such that the area of the inner parallel set \(\Omega ^r\) is equal to \(\pi r^2\) . The proof of the main theorem requires the combination of several intermediate facts, some of which are of interest in their own right. Examples are given demonstrating the generality of the result as well as the sharpness of our assumptions. In particular, as an application of the main theorem, we illustrate how to effectively approximate the Cheeger constant of the Koch snowflake.
      PubDate: 2017-11-01
      DOI: 10.1007/s00526-017-1263-0
      Issue No: Vol. 56, No. 6 (2017)
       
  • Green’s function for elliptic systems: existence and
           Delmotte–Deuschel bounds
    • Authors: Joseph G. Conlon; Arianna Giunti; Felix Otto
      Abstract: This paper is divided into two parts: In the main deterministic part, we prove that for an open domain \(D \subset \mathbb {R}^d\) with \(d \ge 2\) , for every (measurable) uniformly elliptic tensor field a and for almost every point \(y \in D\) , there exists a unique Green’s function centred in y associated to the vectorial operator \(-\nabla \cdot a\nabla \) in D. This result implies the existence of the fundamental solution for elliptic systems when \(d>2\) , i.e. the Green function for \(-\nabla \cdot a\nabla \) in \(\mathbb {R}^d\) . In the second part, we introduce a shift-invariant ensemble \(\langle \cdot \rangle \) over the set of uniformly elliptic tensor fields, and infer for the fundamental solution G some pointwise bounds for \(\langle G(\cdot ; x,y) \rangle \) , \(\langle \nabla _x G(\cdot ; x,y) \rangle \) and \(\langle \nabla _x\nabla _y G(\cdot ; x,y) \rangle \) . These estimates scale optimally in space and provide a generalisation to systems of the bounds obtained by Delmotte and Deuschel for the scalar case.
      PubDate: 2017-10-25
      DOI: 10.1007/s00526-017-1255-0
      Issue No: Vol. 56, No. 6 (2017)
       
  • Minkowski valuations on convex functions
    • Authors: Andrea Colesanti; Monika Ludwig; Fabian Mussnig
      Abstract: A classification of \({\text {SL}}(n)\) contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measure is characterized. In addition, a new \({\text {SL}}(n)\) covariant Minkowski valuation on convex functions is defined and characterized.
      PubDate: 2017-10-23
      DOI: 10.1007/s00526-017-1243-4
      Issue No: Vol. 56, No. 6 (2017)
       
 
 
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