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

Abstract

We show that local weak solutions to parabolic systems of p-Laplace type are Hölder continuous in time with values in a spatial Lebesgue space and Hölder 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.