Regularity of nonlinear equations for fractional Laplacian

DOI10.1090/S0002-9939-2013-11734-XzbMath1279.35023OpenAlexW2000488633MaRDI QIDQ2839350

Aliang Xia, Jianfu Yang

Publication date: 5 July 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2013-11734-x

zbMATH Keywords

regularityfractional Laplacian\(L^\infty\) bounds

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Degenerate elliptic equations (35J70) A priori estimates in context of PDEs (35B45) Weak solutions to PDEs (35D30) Pseudodifferential operators (47G30)

Related Items (9)

Existence of positive solutions for nonlinear fractional Neumann elliptic equations ⋮ Existence and uniqueness of positive solutions to fractional Laplacians with singular nonlinearities ⋮ ON STRONGLY INDEFINITE SYSTEMS INVOLVING FRACTIONAL ELLIPTIC OPERATORS ⋮ On a fractional Kirchhoff type problem with critical exponential growth nonlinearity ⋮ Concentration-compactness principle for nonlocal scalar field equations with critical growth ⋮ Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian ⋮ Multiplicity and concentration results for magnetic relativistic Schrödinger equations ⋮ Existence and uniqueness of weak positive solution for essential singular elliptic problem involving the square root of the Laplacian ⋮ Stability of Positive Solution to Fractional Logistic Equations

Cites Work

• Regularity of radial minimizers and extremal solutions of semilinear elliptic equations
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• Remarks on the Schrödinger operator with singular complex potentials
• Elliptic partial differential equations of second order
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations
• Regularity of the obstacle problem for a fractional power of the laplace operator
• The local regularity of solutions of degenerate elliptic equations
• An Extension Problem Related to the Fractional Laplacian

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