Regularity for obstacle problems to anisotropic parabolic equations

TL;DR

This paper proves local Hölder continuity of solutions to obstacle problems for anisotropic parabolic equations using intrinsic scaling, even when only the obstacle's Hölder continuity is known, advancing regularity theory in this area.

Contribution

It extends regularity results to anisotropic parabolic obstacle problems with minimal assumptions on the obstacle's regularity.

Findings

Established local Hölder continuity of solutions

Applied intrinsic scaling method to anisotropic equations

Reduced regularity assumptions on the obstacle

Abstract

Following Dibenedetto's intrinsic scaling method, we prove local H\"older continuity of weak solutions to obstacle problems related to some anisotropic parabolic equations under the condition for which only H\"older's continuity of the obstacle is known.