On nonlocal quasilinear equations and their local limits

DOI10.1016/j.jde.2016.12.001zbMath1357.35273arXiv1503.06939OpenAlexW1638819079MaRDI QIDQ501636

Espen R. Jakobsen, Emmanuel Chasseigne

Publication date: 9 January 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.06939

zbMATH Keywords

well-posednessviscosity solutionslocal limits\(p\)-Laplaceinfinity-Laplacenonlocal quasilinear equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Integro-partial differential equations (45K05) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Integro-differential operators (47G20) Quasilinear elliptic equations (35J62) Viscosity solutions to PDEs (35D40) Integro-partial differential equations (35R09) Comparison principles in context of PDEs (35B51) Quasilinear parabolic equations (35K59)

Related Items (12)

Comparison principles for nonlocal Hamilton-Jacobi equations ⋮ Evolution driven by the infinity fractional Laplacian ⋮ Long-time asymptotics for a 1D nonlocal porous medium equation with absorption or convection ⋮ Interior regularity results for fractional elliptic equations that degenerate with the gradient ⋮ Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas ⋮ Hölder estimates for viscosity solutions of equations of fractional \(p\)-Laplace type ⋮ Perron's method and Wiener's theorem for a nonlocal equation ⋮ Higher Hölder regularity for the fractional \(p\)-Laplacian in the superquadratic case ⋮ Coupling local and nonlocal evolution equations ⋮ Coupling Lévy measures and comparison principles for viscosity solutions ⋮ Equivalence of solutions to fractional \(p\)-Laplace type equations ⋮ On asymptotic expansions for the fractional infinity Laplacian

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