Hölder regularity for singular parabolic systems of $p$-Laplacian type

Abstract

We study the regularity for nonlinear parabolic systems of $p$-Laplacian type, in the singular case $\frac{{2m}}{{m + 2}}<p<2$. We show an optimal condition on given external forces for a local Höolder continuity. Actually, our main result recovers the classical one for linear equations. The proof is based on Campanato's direct approach with the intrinsic scaling to the evolutionary $p$-Laplace operator. The iteration scheme is performed similarly as in [18], however, with some technical care peculiar to the singular case.