The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour

DOI10.1016/j.na.2020.112034zbMath1447.35205arXiv2004.05799OpenAlexW3036169333MaRDI QIDQ2199973

Juan Luis Vazquez

Publication date: 14 September 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.05799

zbMATH Keywords

fundamental solutionsasymptotic behaviourfractional operators

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Fundamental solutions to PDEs (35A08) Degenerate parabolic equations (35K65) Fractional partial differential equations (35R11) Quasilinear parabolic equations with (p)-Laplacian (35K92)

Related Items (18)

The Cauchy problem for the fast \(p\)-Laplacian evolution equation. Characterization of the global Harnack principle and fine asymptotic behaviour ⋮ Characterisation of homogeneous fractional Sobolev spaces ⋮ Symmetrization for fractional elliptic problems: a direct approach ⋮ Evolution driven by the infinity fractional Laplacian ⋮ Large time behavior for a nonlocal nonlinear gradient flow ⋮ Anisotropic fast diffusion equations ⋮ Self-similar solution for fractional Laplacian in cones ⋮ Asymptotic behaviors for the compressible Euler system with nonlinear velocity alignment ⋮ Qualitative analysis of solutions to a nonlocal Choquard–Kirchhoff diffusion equations in ℝN$$ {\mathbb{R}}^N $$ ⋮ Hölder regularity for parabolic fractional \(p\)-Laplacian ⋮ 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 ⋮ Local boundedness and Hölder continuity for the parabolic fractional \(p\)-Laplace equations ⋮ Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas ⋮ Growing solutions of the fractional \(p\)-Laplacian equation in the fast diffusion range ⋮ The fractional \(p\)-Laplacian evolution equation in \(\mathbb{R}^N\) in the sublinear case ⋮ Regularity theory for mixed local and nonlocal parabolic \(p\)-Laplace equations ⋮ Continuity of solutions to a nonlinear fractional diffusion equation

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