The fractional \(p\)-Laplacian evolution equation in \(\mathbb{R}^N\) in the sublinear case

DOI10.1007/s00526-021-02005-6zbMath1471.35312arXiv2011.01521OpenAlexW3173456577WikidataQ114229006 ScholiaQ114229006MaRDI QIDQ2048708

Juan Luis Vazquez

Publication date: 23 August 2021

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.01521

zbMATH Keywords

global Harnack inequalitiesself-similar fundamental solutionvery singular solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Fundamental solutions to PDEs (35A08) Degenerate parabolic equations (35K65) Initial value problems for second-order parabolic equations (35K15) Fractional partial differential equations (35R11) Quasilinear parabolic equations with (p)-Laplacian (35K92) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (14)

The Cauchy problem for the fast \(p\)-Laplacian evolution equation. Characterization of the global Harnack principle and fine asymptotic behaviour ⋮ Evolution driven by the infinity fractional Laplacian ⋮ Harnack inequality for the nonlocal equations with general growth ⋮ Large time behavior for a nonlocal nonlinear gradient flow ⋮ Anisotropic fast diffusion equations ⋮ Local boundedness of variational solutions to nonlocal double phase parabolic equations ⋮ Higher Hölder regularity for nonlocal parabolic equations with irregular kernels ⋮ Asymptotic behaviors for the compressible Euler system with nonlinear velocity alignment ⋮ Qualitative analysis of solutions to a nonlocal Choquard–Kirchhoff diffusion equations in ℝN$$ {\mathbb{R}}^N $$ ⋮ A Hölder estimate with an optimal tail for nonlocal parabolic \(p\)-Laplace equations ⋮ Fine properties of solutions to the Cauchy problem for a fast diffusion equation with Caffarelli-Kohn-Nirenberg weights ⋮ Growing solutions of the fractional \(p\)-Laplacian equation in the fast diffusion range ⋮ Existence and non-existence of global solutions for a nonlocal Choquard-Kirchhoff diffusion equations in \(\mathbb{R}^N \) ⋮ Regularity theory for mixed local and nonlocal parabolic \(p\)-Laplace equations

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