# On regularity of weak solutions to linear parabolic systems with measurable coefficients

## TL;DR

This paper proves that weak solutions to certain linear parabolic systems with measurable coefficients are locally Hölder continuous in the Lp sense, extending regularity results to systems with minimal coefficient regularity.

## Contribution

It introduces a new regularity property showing weak solutions are locally Hölder continuous in Lp for systems with time and space measurable coefficients.

## Key findings

- Weak solutions are locally Hölder continuous in Lp.
- Regularity holds for coefficients depending measurably on time and all spatial variables.
- Extends regularity theory to more general parabolic systems.

## Abstract

We establish a new regularity property for weak solutions of parabolic systems with coefficients depending measurably on time as well as on all spatial variables. Namely, weak solutions are locally H{\"o}lder continuous Lp valued functions for some p > 2.