Local boundedness of solutions to non-local parabolic equations modeled on the fractional \(p\)-Laplacian

DOI10.1016/J.JDE.2018.12.021zbMath1445.35093arXiv1712.04061OpenAlexW2908353192WikidataQ128679683 ScholiaQ128679683MaRDI QIDQ1733219

Martin Strömqvist

Publication date: 21 March 2019

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

Full work available at URL: https://arxiv.org/abs/1712.04061

zbMATH Keywords

local boundednessCaccioppoli estimatesintrinsic geometryquasilinear parabolic non-local operators

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) Fractional partial differential equations (35R11) Quasilinear parabolic equations with (p)-Laplacian (35K92)

Related Items (27)

Regularity estimates for fractional orthotropic \(p\)-Laplacians of mixed order ⋮ Some local properties of subsolution and supersolutions for a doubly nonlinear nonlocal \(p\)-Laplace equation ⋮ Harnack inequality for the nonlocal equations with general growth ⋮ Regularity of weak solutions for mixed local and nonlocal double phase parabolic equations ⋮ Harnack's estimate for a mixed local-nonlocal doubly nonlinear parabolic equation ⋮ Large time behavior for a nonlocal nonlinear gradient flow ⋮ Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations ⋮ Local boundedness of variational solutions to nonlocal double phase parabolic equations ⋮ Higher Hölder regularity for nonlocal parabolic equations with irregular kernels ⋮ Harnack inequality for mixed local and nonlocal parabolic \(p\)-Laplace equations ⋮ Hölder regularity for parabolic fractional \(p\)-Laplacian ⋮ A Hölder estimate with an optimal tail for nonlocal parabolic \(p\)-Laplace equations ⋮ On the weak Harnack estimate for nonlocal equations ⋮ Boundary regularity estimates for the nonlocal normalized \(p\)-Laplacian in different kind of domains ⋮ The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour ⋮ Unnamed Item ⋮ Local boundedness and Hölder continuity for the parabolic fractional \(p\)-Laplace equations ⋮ Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas ⋮ Nonlocal operators with singular anisotropic kernels ⋮ The fractional \(p\)-Laplacian evolution equation in \(\mathbb{R}^N\) in the sublinear case ⋮ Nonlocal diffusion equations with dynamical boundary conditions ⋮ Regularity theory for mixed local and nonlocal parabolic \(p\)-Laplace equations ⋮ Continuity of solutions to a nonlinear fractional diffusion equation ⋮ Existence of variational solutions to doubly nonlinear nonlocal evolution equations via minimizing movements ⋮ Local boundedness of a mixed local-nonlocal doubly nonlinear equation ⋮ Hölder regularity for mixed local and nonlocal \(p\)-Laplace parabolic equations ⋮ Existence of variational solutions to nonlocal evolution equations via convex minimization

Cites Work

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• Hölder estimates and large time behavior for a nonlocal doubly nonlinear evolution
• Local behavior of fractional \(p\)-minimizers
• Nonlocal Harnack inequalities
• Hitchhiker's guide to the fractional Sobolev spaces
• Optimal existence and uniqueness theory for the fractional heat equation
• Hölder estimates for viscosity solutions of equations of fractional \(p\)-Laplace type
• Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes
• Degenerate parabolic equations
• Harnack estimates for quasi-linear degenerate parabolic differential equations
• Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps
• Harnack's inequality for stable Lévy processes
• Higher Hölder regularity for the fractional \(p\)-Laplacian in the superquadratic case
• A class of integral equations and approximation of \(p\)-Laplace equations
• Harnack estimates for degenerate parabolic equations modeled on the subelliptic \(p\)-Laplacian
• The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation
• Local Regularity for Parabolic Nonlocal Operators
• Regularity theory for parabolic nonlinear integral operators
• Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations
• Regularity results for nonlocal parabolic equations

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