Regularity and rigidity theorems for a class of anisotropic nonlocal operators

DOI10.1007/s00229-016-0875-6zbMathNonearXiv1512.06509OpenAlexW3105587172MaRDI QIDQ527700

Alberto Farina, Enrico Valdinoci

Publication date: 12 May 2017

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.06509

Mathematics Subject Classification ID

Fractional partial differential equations (35R11) Integro-partial differential equations (35R09) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items

Mixed local and nonlocal elliptic operators: regularity and maximum principles ⋮ Liouville-type theorem for a nonlocal operator on the half plane ⋮ Liouville results for fully nonlinear integral elliptic equations in exterior domains ⋮ Decay Estimates in Time for Classical and Anomalous Diffusion ⋮ Existence of solutions of a class of nonlinear nonlocal problems involving the potential ⋮ Decay estimates for evolutionary equations with fractional time-diffusion ⋮ On a class of Kirchhoff equations involving an anisotropic operator and potential ⋮ Positive and nodal solutions of the generalized BO-ZK equation ⋮ Three nontrivial solutions for a nonlinear anisotropic nonlocal equation ⋮ Gradient estimates for a class of anisotropic nonlocal operators ⋮ Fractional thoughts ⋮ Definition of fractional Laplacian for functions with polynomial growth

Cites Work

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• Hitchhiker's guide to the fractional Sobolev spaces
• The Dirichlet problem for nonlocal operators with singular kernels: convex and nonconvex domains
• Fractional calculus for power functions and eigenvalues of the fractional Laplacian
• Interior estimates for second-order elliptic differential (or finite- difference) equations via the maximum principle
• Pohozaev identities for anisotropic integrodifferential operators