Holder Regularity for the Gradients of Solutions of Degenerate Parabolic Systems

Abstract

We study a class of parabolic systems of the form vt = div(F(|Dv|Dv). The function F satisfies a few technical hypotheses which are satisfied, for example, by F(s) = sⁿ⁻² with n > 1. Hence our results extend the standard results for the parabolic p-Laplacian operator. The method of proof is similar to the usual one but uses some new ideas about Poincar´e-type inequalities and a special Gehring inequality.