Gradient higher integrability for degenerate parabolic double-phase systems

TL;DR

This paper establishes local higher integrability of the gradient for solutions to degenerate parabolic double-phase systems, providing reverse Hölder estimates using intrinsic geometry and stopping time techniques.

Contribution

It introduces a novel approach to prove higher integrability for double-phase systems in the parabolic setting, extending existing regularity results.

Findings

Proved local higher integrability of the gradient.

Established reverse Hölder estimates for the gradient.

Utilized intrinsic geometry and stopping time arguments.

Abstract

We prove local higher integrability of the gradient of a weak solution to a degenerate parabolic double-phase system. This result comes with a reverse H\"older type estimate for the gradient. The proof is based on estimates in the intrinsic geometry and stopping time arguments.