Optimal regularity for the porous medium equation

TL;DR

This paper establishes the best possible regularity results for solutions to the porous medium equation using velocity averaging, aligning with the optimal regularity known for the linear case.

Contribution

It introduces a novel approach to prove optimal Sobolev regularity for porous medium equations, extending linear regularity results to nonlinear settings.

Findings

Proves optimal Sobolev regularity for solutions.

Uses velocity averaging techniques effectively.

Results match linear case regularity.

Abstract

We prove optimal regularity for solutions to porous media equations in Sobolev spaces, based on velocity averaging techniques. In particular, the obtained regularity is consistent with the optimal regularity in the linear limit.