Almost everywhere H\"older continuity of gradients to non-diagonal parabolic systems

TL;DR

This paper proves that solutions to a broad class of nonlinear non-diagonal parabolic systems have gradients that are almost everywhere H"older continuous, enhancing understanding of their regularity properties.

Contribution

It establishes a local almost everywhere regularity result for nonlinear non-diagonal parabolic systems depending on the symmetric gradient.

Findings

Gradients are almost everywhere H"older continuous.

Regularity result applies to general nonlinear non-diagonal systems.

Advances understanding of solution smoothness in complex parabolic PDEs.

Abstract

We present a local almost everywhere regularity result for a general nonlinear non-diagonal parabolic system, which main part depends on symmetric part of the gradient.