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MATHEMATICS (656 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: 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: 21)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 7)
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: 1)
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: 7)
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: 9)
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 Network Science     Open Access  
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: 19)
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  
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: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
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: 18)
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)
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)
Fixed Point Theory and Applications     Open Access   (Followers: 1)

        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  [2353 journals]
  • On Neumann problems for nonlocal Hamilton–Jacobi equations with
           dominating gradient terms
    • Authors: Daria Ghilli
      Abstract: Abstract We are concerned with the well-posedness of Neumann boundary value problems for nonlocal Hamilton–Jacobi equations related to jump processes in general smooth domains. We consider a nonlocal diffusive term of censored type of order strictly less than 1 and Hamiltonians both in coercive form and in noncoercive Bellman form, whose growth in the gradient make them the leading term in the equation. We prove a comparison principle for bounded sub-and supersolutions in the context of viscosity solutions with generalized boundary conditions, and consequently by Perron’s method we get the existence and uniqueness of continuous solutions. We give some applications in the evolutive setting, proving the large time behaviour of the associated evolutive problem under suitable assumptions on the data.
      PubDate: 2017-09-01
      DOI: 10.1007/s00526-017-1225-6
      Issue No: Vol. 56, No. 5 (2017)
  • A quantitative form of Faber–Krahn inequality
    • Authors: Nicola Fusco; Yi Ru-Ya Zhang
      Abstract: Abstract The Faber–Krahn inequality states that balls are the unique minimizers of the first eigenvalue of the p-Laplacian among all sets with fixed volume. In this paper we prove a sharp quantitative form of this inequality. This extends to the case \(p>1\) a recent result proved by Brasco et al. (Duke Math J 164:1777–1831, 2015) for the Laplacian.
      PubDate: 2017-08-30
      DOI: 10.1007/s00526-017-1224-7
      Issue No: Vol. 56, No. 5 (2017)
  • Optimal lower exponent for the higher gradient integrability of solutions
           to two-phase elliptic equations in two dimensions
    • Authors: Silvio Fanzon; Mariapia Palombaro
      Abstract: Abstract We study the higher gradient integrability of distributional solutions u to the equation \({{\mathrm{div}}}(\sigma \nabla u) = 0\) in dimension two, in the case when the essential range of \(\sigma \) consists of only two elliptic matrices, i.e., \(\sigma \in \{\sigma _1, \sigma _2\}\) a.e. in \(\Omega \) . In Nesi et al. (Ann Inst H Poincaré Anal Non Linéaire 31(3):615–638, 2014), for every pair of elliptic matrices \(\sigma _1\) and \(\sigma _2\) , exponents \(p_{\sigma _1,\sigma _2}\in (2,+\infty )\) and \(q_{\sigma _1,\sigma _2}\in (1,2)\) have been found so that if \(u\in W^{1,q_{\sigma _1,\sigma _2}}(\Omega )\) is solution to the elliptic equation then \(\nabla u\in L^{p_{\sigma _1,\sigma _2}}_{\mathrm{weak}}(\Omega )\) and the optimality of the upper exponent \(p_{\sigma _1,\sigma _2}\) has been proved. In this paper we complement the above result by proving the optimality of the lower exponent \(q_{\sigma _1,\sigma _2}\) . Precisely, we show that for every arbitrarily small \(\delta \) , one can find a particular microgeometry, i.e., an arrangement of the sets \(\sigma ^{-1}(\sigma _1)\) and \(\sigma ^{-1}(\sigma _2)\) , for which there exists a solution u to the corresponding elliptic equation such that \(\nabla u \in L^{q_{\sigma _1,\sigma _2}-\delta }\) , but \(\nabla u \notin L^{q_{\sigma _1,\sigma _2}}\) . The existence of such optimal microgeometries is achieved by convex integration methods, adapting to the present setting the geometric constructions provided in Astala et al. (Ann Scuola Norm Sup Pisa Cl Sci 5(7):1–50, 2008) for the isotropic case.
      PubDate: 2017-08-29
      DOI: 10.1007/s00526-017-1222-9
      Issue No: Vol. 56, No. 5 (2017)
  • Collision of incompressible inviscid fluids effluxing from two nozzles
    • Authors: Lili Du; Yongfu Wang
      Abstract: Abstract This paper concerns the mathematical theory of the collision problem of two-dimensional incompressible inviscid fluids issuing from two given nozzles. The main result reads that for given two co-axis symmetric semi-infinitely long nozzles with arbitrary variable sections, imposing the incoming mass fluxes in two nozzles, there exists a smooth impinging outgoing jet, such that the two free boundaries of the impinging jet initiate smoothly at the endpoints of the nozzles and approach to some asymptotic direction in downstream, and the pressure on the free surface remains a constant. Furthermore, we show that there exists a unique smooth surface separating the two nonmiscible fluids and there exists a unique stagnation point in the fluid region and its closure. Moreover, some results on the uniqueness and the estimates of the location of the impinging outgoing jet are also established. Finally, the asymptotic behaviors, the precise estimate to the deflection angle and other properties to the impinging outgoing jet are also considered.
      PubDate: 2017-08-28
      DOI: 10.1007/s00526-017-1221-x
      Issue No: Vol. 56, No. 5 (2017)
  • Existence and multiplicity of positive solutions to Schrödinger–Poisson
           type systems with critical nonlocal term
    • Authors: Yuhua Li; Fuyi Li; Junping Shi
      Abstract: Abstract The existence, nonexistence and multiplicity of positive radially symmetric solutions to a class of Schrödinger–Poisson type systems with critical nonlocal term are studied with variational methods. The existence of both the ground state solution and mountain pass type solutions are proved. It is shown that the parameter ranges of existence and nonexistence of positive solutions for the critical nonlocal case are completely different from the ones for the subcritical nonlocal system.
      PubDate: 2017-08-24
      DOI: 10.1007/s00526-017-1229-2
      Issue No: Vol. 56, No. 5 (2017)
  • Uniform Lipschitz regularity of flat segregated interfaces in a singularly
           perturbed problem
    • Authors: Kelei Wang
      Abstract: Abstract For the singularly perturbed system $$\begin{aligned} \varDelta u_{i,\beta }=\beta u_{i,\beta }\sum _{j\ne i}u_{j,\beta }^2, \quad 1\le i\le N, \end{aligned}$$ we prove that flat segregated interfaces are uniformly Lipschitz as \(\beta \rightarrow +\infty \) . As a byproduct of the proof we also obtain the optimal lower bound near flat interfaces, $$\begin{aligned} \sum _iu_{i,\beta }\ge c\beta ^{-1/4}. \end{aligned}$$ .
      PubDate: 2017-08-24
      DOI: 10.1007/s00526-017-1235-4
      Issue No: Vol. 56, No. 5 (2017)
  • Universal inequality and upper bounds of eigenvalues for non-integer
           poly-Laplacian on a bounded domain
    • Authors: Hua Chen; Ao Zeng
      Abstract: Abstract In this paper we first study the universal inequality which is related to the eigenvalues of the fractional Laplacian \((-\Delta )^s _{\Omega }\) for \(s>0\) and \(s\in \mathbb {Q}_+\) . Here \(\Omega \subset \mathbb {R}^n\) is a bounded open domain, and \(\mathbb {Q}_+\) is the set of all positive rational numbers. Secondly, if \(s\in \mathbb {Q}_+\) and \(s\ge 1\) (in this case, the operator is also called the non-integer poly-Laplacian), then by this universal inequality and the variant of Chebyshev sum inequality, we can deduce the so-called Yang type inequality for the corresponding eigenvalue problem, which is the extension to the case of poly-Laplacian operators. Finally, we can get the upper bounds of the corresponding eigenvalues from the Yang type inequality.
      PubDate: 2017-08-23
      DOI: 10.1007/s00526-017-1220-y
      Issue No: Vol. 56, No. 5 (2017)
  • Global dynamics of the Lotka–Volterra competition–diffusion system
           with equal amount of total resources, III
    • Authors: Xiaoqing He; Wei-Ming Ni
      Abstract: Abstract In this paper—Part III of this series of three papers, we continue to investigate the joint effects of diffusion and spatial concentration on the global dynamics of the classical Lotka–Volterra competition–diffusion system. To further illustrate the general results obtained in Part I (He and Ni in Commun Pure Appl Math 69:981–1014, 2016. doi:10.1002/cpa.21596), we have focused on the case when the two competing species have identical competition abilities and the same amount of total resources. In contrast to Part II (He and Ni in Calc Var Partial Differ Equ 2016. doi:10.1007/s00526-016-0964-0), our results here show that in case both species have spatially heterogeneous distributions of resources, the outcome of the competition is independent of initial values but depends solely on the dispersal rates, which in turn depends on the distribution profiles of the resources—thereby extending the celebrated phenomenon “slower diffuser always prevails!” Furthermore, the species with a “sharper” spatial concentration in its distribution of resources seems to have the edge of competition advantage. Limiting behaviors of the globally asymptotically stable steady states are also obtained under various circumstances in terms of dispersal rates.
      PubDate: 2017-08-23
      DOI: 10.1007/s00526-017-1234-5
      Issue No: Vol. 56, No. 5 (2017)
  • Defects of liquid crystals with variable degree of orientation
    • Authors: Onur Alper; Robert Hardt; Fang-Hua Lin
      Abstract: Abstract The defect set of minimizers of the modified Ericksen energy for nematic liquid crystals consists locally of a finite union of isolated points and Hölder continuous curves with finitely many crossings.
      PubDate: 2017-08-23
      DOI: 10.1007/s00526-017-1218-5
      Issue No: Vol. 56, No. 5 (2017)
  • Normalized bound states for the nonlinear Schrödinger equation in
           bounded domains
    • Authors: Dario Pierotti; Gianmaria Verzini
      Abstract: Abstract Given \(\rho >0\) , we study the elliptic problem $$\begin{aligned} \text {find } (U,\lambda )\in H^1_0(\Omega )\times {\mathbb {R}}\text { such that } {\left\{ \begin{array}{ll} -\Delta U+\lambda U= U ^{p-1}U\\ \int _{\Omega } U^2\, dx=\rho , \end{array}\right. } \end{aligned}$$ where \(\Omega \subset {\mathbb {R}}^N\) is a bounded domain and \(p>1\) is Sobolev-subcritical, searching for conditions (about \(\rho \) , N and p) for the existence of solutions. By the Gagliardo-Nirenberg inequality it follows that, when p is \(L^2\) -subcritical, i.e. \(1<p<1+4/N\) , the problem admits solutions for every \(\rho >0\) . In the \(L^2\) -critical and supercritical case, i.e. when \(1+4/N \le p < 2^*-1\) , we show that, for any \(k\in {\mathbb {N}}\) , the problem admits solutions having Morse index bounded above by k only if \(\rho \) is sufficiently small. Next we provide existence results for certain ranges of \(\rho \) , which can be estimated in terms of the Dirichlet eigenvalues of \(-\Delta \) in \(H^1_0(\Omega )\) , extending to changing sign solutions and to general domains some results obtained in Noris et al. in Anal. PDE 7:1807–1838, 2014 for positive solutions in the ball.
      PubDate: 2017-08-23
      DOI: 10.1007/s00526-017-1232-7
      Issue No: Vol. 56, No. 5 (2017)
  • Optimal regularity for the thin obstacle problem with $$C^{0,\alpha }$$ C
           0 , α coefficients
    • Authors: Angkana Rüland; Wenhui Shi
      Abstract: Abstract In this article we study solutions to the (interior) thin obstacle problem under low regularity assumptions on the coefficients, the obstacle and the underlying manifold. Combining the linearization method of Andersson (Invent Math 204(1):1–82, 2016. doi:10.1007/s00222-015-0608-6) and the epiperimetric inequality from Focardi and Spadaro (Adv Differ Equ 21(1–2):153–200, 2016), Garofalo, Petrosyan and Smit Vega Garcia (J Math Pures Appl 105(6):745–787, 2016. doi:10.1016/j.matpur.2015.11.013), we prove the optimal \(C^{1,\min \{\alpha ,1/2\}}\) regularity of solutions in the presence of \(C^{0,\alpha }\) coefficients \(a^{ij}\) and \(C^{1,\alpha }\) obstacles \(\phi \) . Moreover we investigate the regularity of the regular free boundary and show that it has the structure of a \(C^{1,\gamma }\) manifold for some \(\gamma \in (0,1)\) .
      PubDate: 2017-08-23
      DOI: 10.1007/s00526-017-1230-9
      Issue No: Vol. 56, No. 5 (2017)
  • Decay of superconductivity away from the magnetic zero set
    • Authors: Bernard Helffer; Ayman Kachmar
      Abstract: Abstract We establish exponential bounds on the Ginzburg–Landau order parameter away from the curve where the applied magnetic field vanishes. In the units used in this paper, the estimates are valid when the parameter measuring the strength of the applied magnetic field is comparable with the Ginzburg–Landau parameter. This completes a previous work by the authors analyzing the case when this strength was much higher. Our results display the distribution of surface and bulk superconductivity and are valid under the assumption that the magnetic field is Hölder continuous.
      PubDate: 2017-08-23
      DOI: 10.1007/s00526-017-1226-5
      Issue No: Vol. 56, No. 5 (2017)
  • On the interior regularity of weak solutions to the 2-D incompressible
           Euler equations
    • Authors: Juhana Siljander; José Miguel Urbano
      Abstract: Abstract We study whether some of the non-physical properties observed for weak solutions of the incompressible Euler equations can be ruled out by studying the vorticity formulation. Our main contribution is in developing an interior regularity method in the spirit of De Giorgi–Nash–Moser, showing that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity result $$\begin{aligned} u \in L_\mathrm{loc}^{2+\varepsilon }(\Omega _T) \implies \mathrm{local\ regularity} \end{aligned}$$ for weak solutions in the energy space \(L_t^\infty L_x^2\) , satisfying appropriate vorticity estimates. We also obtain improved integrability for the vorticity—which is to be compared with the DiPerna–Lions assumptions. The argument is completely local in nature as the result follows from the structural properties of the equation alone, while completely avoiding all sorts of boundary conditions and related gradient estimates. To the best of our knowledge, the approach we follow is new in the context of Euler equations and provides an alternative look at interior regularity issues. We also show how our method can be used to give a modified proof of the classical Serrin condition for the regularity of the Navier–Stokes equations in any dimension.
      PubDate: 2017-08-21
      DOI: 10.1007/s00526-017-1231-8
      Issue No: Vol. 56, No. 5 (2017)
  • Interior Sobolev regularity for fully nonlinear parabolic equations
    • Authors: Ricardo Castillo; Edgard A. Pimentel
      Abstract: Abstract In the present paper, we establish sharp Sobolev estimates for solutions of fully nonlinear parabolic equations, under minimal, asymptotic, assumptions on the governing operator. In particular, we prove that solutions are in \(W^{2,1;p}_{ loc }\) . Our argument unfolds by importing improved regularity from a limiting configuration. In this concrete case, we recur to the recession function associated with F. This machinery allows us to impose conditions solely on the original operator at the infinity of \(\mathcal {S}(d)\) . From a heuristic viewpoint, integral regularity would be set by the behavior of F at the ends of that space. Moreover, we explore a number of consequences of our findings, and develop some related results; these include a parabolic version of Escauriaza’s exponent, a universal modulus of continuity for the solutions and estimates in p-BMO spaces.
      PubDate: 2017-08-21
      DOI: 10.1007/s00526-017-1227-4
      Issue No: Vol. 56, No. 5 (2017)
  • Generalized characteristics and Lax–Oleinik operators: global theory
    • Authors: Piermarco Cannarsa; Wei Cheng
      Abstract: Abstract For autonomous Tonelli systems on \(\mathbb {R}^n\) , we develop an intrinsic proof of the existence of generalized characteristics using sup-convolutions. This approach, together with convexity estimates for the fundamental solution, leads to new results such as the global propagation of singularities along generalized characteristics.
      PubDate: 2017-08-21
      DOI: 10.1007/s00526-017-1219-4
      Issue No: Vol. 56, No. 5 (2017)
  • Global properties of Dirichlet forms in terms of Green’s formula
    • Authors: Sebastian Haeseler; Matthias Keller; Daniel Lenz; Jun Masamune; Marcel Schmidt
      Abstract: Abstract We study global properties of Dirichlet forms such as uniqueness of the Dirichlet extension, stochastic completeness and recurrence. We characterize these properties by means of vanishing of a boundary term in Green’s formula for functions from suitable function spaces and suitable operators arising from extensions of the underlying form. We first present results in the framework of general Dirichlet forms on \(\sigma \) -finite measure spaces. For regular Dirichlet forms our results can be strengthened as all operators from the previous considerations turn out to be restrictions of a single operator. Finally, the results are applied to graphs, weighted manifolds, and metric graphs, where the operators under investigation can be determined rather explicitly, and certain volume growth criteria can be (re)derived.
      PubDate: 2017-08-05
      DOI: 10.1007/s00526-017-1216-7
      Issue No: Vol. 56, No. 5 (2017)
  • General methods of elliptic minimization
    • Authors: J. Harrison; H. Pugh
      Abstract: Abstract We provide general methods in the calculus of variations for the anisotropic Plateau problem in arbitrary dimension and codimension. Given a collection of competing “surfaces” that span a given “bounding set” in an ambient metric space, we produce one minimizing an elliptic area functional. The collection of competing surfaces is assumed to satisfy a set of geometrically-defined axioms. These axioms hold for collections defined using any combination of homological, cohomological or linking number spanning conditions. A variety of minimization problems can be solved, including sliding boundaries.
      PubDate: 2017-08-03
      DOI: 10.1007/s00526-017-1217-6
      Issue No: Vol. 56, No. 4 (2017)
  • A multidimensional Birkhoff theorem for time-dependent Tonelli
    • Authors: Marie-Claude Arnaud; Andrea Venturelli
      Abstract: Abstract Let M be a closed and connected manifold, \(H:T^*M\times {{\mathbb {R}}}/\mathbb {Z}\rightarrow \mathbb {R}\) a Tonelli 1-periodic Hamiltonian and \({\mathscr {L}}\subset T^*M\) a Lagrangian submanifold Hamiltonianly isotopic to the zero section. We prove that if \({\mathscr {L}}\) is invariant by the time-one map of H, then \({\mathscr {L}}\) is a graph over M. An interesting consequence in the autonomous case is that in this case, \({\mathscr {L}}\) is invariant by all the time t maps of the Hamiltonian flow of H.
      PubDate: 2017-07-21
      DOI: 10.1007/s00526-017-1210-0
      Issue No: Vol. 56, No. 4 (2017)
  • Some remarks on the classification of global solutions with asymptotically
           flat level sets
    • Abstract: Abstract We simplify some technical steps from Savin (Ann Math. (2) 169(1):41–78, 2009) in which a conjecture of De Giorgi was addressed. For completeness we make the paper self-contained and reprove the classification of certain global bounded solutions for semilinear equations of the type $$\begin{aligned} \triangle u=W^{\prime }(u), \end{aligned}$$ where W is a double well potential.
      PubDate: 2017-09-08
      DOI: 10.1007/s00526-017-1228-3
  • A chromaticity-brightness model for color images denoising in a Meyer’s
           “u + v” framework
    • Abstract: Abstract A variational model for imaging segmentation and denoising color images is proposed. The model combines Meyer’s “u+v” decomposition with a chromaticity-brightness framework and is expressed by a minimization of energy integral functionals depending on a small parameter \(\varepsilon >0\) . The asymptotic behavior as \(\varepsilon \rightarrow 0^+\) is characterized, and convergence of infima, almost minimizers, and energies are established. In particular, an integral representation of the lower semicontinuous envelope, with respect to the \(L^1\) -norm, of functionals with linear growth and defined for maps taking values on a certain compact manifold is provided. This study escapes the realm of previous results since the underlying manifold has boundary, and the integrand and its recession function fail to satisfy hypotheses commonly assumed in the literature. The main tools are \(\Gamma \) -convergence and relaxation techniques.
      PubDate: 2017-09-07
      DOI: 10.1007/s00526-017-1223-8
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