Local boundedness for weak solutions to fractional porous medium equation

TL;DR

This paper proves that solutions to fractional porous medium equations are locally bounded under optimal conditions, advancing understanding of their regularity in the fast diffusion regime.

Contribution

It introduces new local boundedness results for fractional porous medium equations under optimal tail assumptions, a significant step in regularity theory.

Findings

Solutions are locally bounded in the fast diffusion regime

Optimal tail conditions are sufficient for boundedness

Advances regularity understanding of fractional porous medium equations

Abstract

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