# Global regularity for degenerate/singular parabolic equations involving measure data

## TL;DR

This paper establishes global regularity estimates for solutions to degenerate and singular parabolic equations with measure data, using a novel fractional maximal function approach in nonsmooth domains.

## Contribution

It introduces an innovative fractional maximal function technique to obtain regularity estimates for measure data problems in degenerate and singular parabolic equations.

## Key findings

- Global gradient regularity estimates achieved
- Applicable to nonsmooth bounded domains
- New tool based on fractional maximal functions

## Abstract

We consider degenerate and singular parabolic equations with $p$-Laplacian structure in bounded nonsmooth domains when the right-hand side is a signed Radon measure with finite total mass. We develop a new tool that allows global regularity estimates for the spatial gradient of solutions to such parabolic measure data problems, by introducing the (intrinsic) fractional maximal function of a given measure.