On the H\"older regularity for obstacle problems to porous medium type equations

TL;DR

This paper proves that solutions to obstacle problems with porous medium type equations are locally H"older continuous if the obstacle is H"older continuous, advancing understanding of regularity in nonlinear parabolic problems.

Contribution

It establishes the local H"older regularity of solutions to porous medium obstacle problems under H"older continuous obstacles, a novel regularity result in this context.

Findings

Solutions are locally H"older continuous

Regularity depends on obstacle's H"older continuity

Advances understanding of nonlinear parabolic obstacle problems

Abstract

We show that signed weak solutions to parabolic obstacle problems with porous medium type structure are locally H\"older continuous, provided that the obstacle is H\"older continuous.