Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels

DOI10.1007/s00229-011-0516-zzbMath1258.47064arXiv1011.3565OpenAlexW2073339457MaRDI QIDQ692610

Ki-Ahm Lee, Yong-Cheol Kim

Publication date: 6 December 2012

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

Full work available at URL: https://arxiv.org/abs/1011.3565

zbMATH Keywords

Hölder regularityintegro-differential operatorsviscosity solutionsHarnack estimatesAlexandroff-Backelman-Pucci estimate

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Integro-partial differential equations (45K05) Nonlinear elliptic equations (35J60) Integro-differential operators (47G20) Viscosity solutions to PDEs (35D40)

Related Items

Regularity for fully nonlinear integro-differential operators with regularly varying kernels ⋮ Global Lorentz estimates with variable power to linear parabolic integro-differential equations ⋮ Regularity results for fully nonlinear parabolic integro-differential operators ⋮ Boundary regularity for nonlocal operators with kernels of variable orders ⋮ Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels: subcritical case ⋮ Regularity for solutions of nonlocal, nonsymmetric equations ⋮ Regularity for fully nonlinear equations driven by spatial-inhomogeneous nonlocal operators ⋮ The Evans-Krylov theorem for nonlocal parabolic fully nonlinear equations ⋮ Monotone systems involving variable-order nonlocal operators

Cites Work

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• The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
• Harnack inequality for some classes of Markov processes
• Harnack inequalities for jump processes
• Regularity for solutions of nonlocal, nonsymmetric equations
• Non-local Dirichlet forms and symmetric jump processes
• Regularity theory for fully nonlinear integro-differential equations
• Harnack inequalities for non-local operators of variable order
• Holder estimates for solutions of integro differential equations like the fractional laplace
• Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order