Gradient regularity for a singular parabolic equation in non-divergence form

Abstract

In this paper we consider viscosity solutions of a class of non-homogeneous singular parabolic equations $${\partial }_{t}u-|Du{|}^{\gamma }{\Delta }_p^{N}u=f,$$ where $-1<\gamma <0$, $1<p<\infty$, and $f$ is a given bounded function. We establish interior Hölder regularity of the gradient by studying two alternatives: The first alternative uses an iteration which is based on an approximation lemma. In the second alternative we use a small perturbation argument.

18 pages