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Local boundedness for weak solutions to fractional porous medium equation

Filomena De Filippis

Abstract

We establish local boundedness for solutions to fractional porous medium-type equations in the fast diffusion regime, under optimal tail assumptions.

Local boundedness for weak solutions to fractional porous medium equation

Abstract

We establish local boundedness for solutions to fractional porous medium-type equations in the fast diffusion regime, under optimal tail assumptions.
Paper Structure (4 sections, 7 theorems, 134 equations)

This paper contains 4 sections, 7 theorems, 134 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Caccioppoli estimate
  4. $L^\infty$-estimates

Key Result

Theorem 1.1

Let $u$ be a local, nonnegative, weak sub-solution to pm in $\Omega_T$. If then $u$ is locally bounded.

Theorems & Definitions (12)

  • Theorem 1.1
  • Theorem 1.2
  • Remark 1.1
  • Definition 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • Lemma 2.5: Parabolic embedding
  • Proposition 2.6: Caccioppoli estimate
  • proof : Proof of Proposition \ref{['pca']}
  • ...and 2 more