Gradient Hölder regularity for nonlinear parabolic systems of $p$-Laplacian type

Abstract

We study the Hölder regularity of the spatial gradient of solutions for nonlinear parabolic systems of $p$-Laplacian type in the degenerate and singular cases $ \frac{{2m}}{{m + 2}} < p < \infty$. We obtain an optimal like criterion to gradient Hölder continuity for the right-hand side terms.