Note on time-regularity for weak solutions to parabolic systems of p-Laplace type

TL;DR

This paper proves that weak solutions to certain parabolic p-Laplace systems are temporally Hölder continuous in space and on almost every time line, using a straightforward proof based on higher integrability results.

Contribution

It establishes time-regularity of weak solutions to p-Laplace parabolic systems with a simple, self-contained proof leveraging existing higher integrability results.

Findings

Weak solutions are Hölder continuous in time with spatial Lebesgue values.

Solutions are Hölder continuous on almost every time line.

The proof is elementary and self-contained.

Abstract

We show that local weak solutions to parabolic systems of p-Laplace type are H{\"o}lder continuous in time with values in a spatial Lebesgue space and H{\"o}lder continuous on almost every time line. We provide an elementary and self-contained proof building on the local higher integrability result of Kinnunen and Lewis.