Continuity of solutions to a nonlinear fractional diffusion equation

DOI10.1007/s00028-021-00721-2zbMath1486.35084arXiv1907.00910OpenAlexW3170160446MaRDI QIDQ2064550

Erik Lindgren, Martin Strömqvist, Lorenzo Brasco

Publication date: 6 January 2022

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

Full work available at URL: https://arxiv.org/abs/1907.00910

zbMATH Keywords

Hölder continuitynonlocal parabolic equationsfractional \(p\)-LaplacianMoser's iterative technique

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Fractional partial differential equations (35R11) Quasilinear parabolic equations with (p)-Laplacian (35K92) Comparison principles in context of PDEs (35B51)

Related Items (21)

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 ⋮ Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities ⋮ 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 ⋮ Gradient Hölder regularity in mixed local and nonlocal linear parabolic problem ⋮ Harnack inequality for mixed local and nonlocal parabolic \(p\)-Laplace equations ⋮ A stability result of a fractional heat equation and time fractional diffusion equations governed by fractional fluxes in the Heisenberg group ⋮ Hölder regularity for parabolic fractional \(p\)-Laplacian ⋮ A Hölder estimate with an optimal tail for nonlocal parabolic \(p\)-Laplace equations ⋮ Weak Harnack inequality for a mixed local and nonlocal parabolic equation ⋮ Local properties for weak solutions of nonlocal heat equations ⋮ Regularity theory for mixed local and nonlocal parabolic \(p\)-Laplace equations ⋮ 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

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local Lipschitz continuity of the inverse of the fractional \(p\)-Laplacian, Hölder type continuity and continuous dependence of solutions to associated parabolic equations on bounded domains
• Fractional \(p\)-Laplacian evolution equations
• The second eigenvalue of the fractional \(p\)-Laplacian
• Hölder estimates and large time behavior for a nonlocal doubly nonlinear evolution
• Local behavior of fractional \(p\)-minimizers
• Higher Sobolev regularity for the fractional \(p\)-Laplace equation in the superquadratic case
• Nonlinear commutators for the fractional \(p\)-Laplacian and applications
• Nonlocal Harnack inequalities
• Global Hölder regularity for the fractional \(p\)-Laplacian
• 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
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Hölder continuity for integro-differential parabolic equations with polynomial growth respect to the gradient
• Local boundedness of solutions to non-local parabolic equations modeled on the fractional \(p\)-Laplacian
• Higher Hölder regularity for the fractional \(p\)-Laplacian in the superquadratic case
• Fine boundary regularity for the degenerate fractional \(p\)-Laplacian
• The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour
• Harnack's inequality for parabolic nonlocal equations
• Nonlocal self-improving properties
• Nonlocal equations with measure data
• Regularity for solutions of nonlocal parabolic equations. II
• A class of integral equations and approximation of \(p\)-Laplace equations
• On fractional \(p\)-Laplacian parabolic problem with general data
• Spazi \({\mathcal L}^{(p,\vartheta)} (\Omega,\delta)\) e loro proprieta
• The obstacle problem for nonlinear integro-differential operators
• The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation
• Regularity for solutions of non local parabolic equations
• Global gradient bounds for the parabolicp-Laplacian system
• Harnack's Inequality for Degenerate and Singular Parabolic Equations
• On the Evolutionary Fractionalp-Laplacian
• Hölder estimates for advection fractional-diffusion equations

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