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 equationsand 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.

Gradient Holder regularity for parabolic normalized p(x,t)-Laplace equation

“…with −1 < γ < ∞ and 1 < p < ∞, the local higher regularity properties of solutions to (1.6) have been studied in [1,2,5], provided that f is bounded and continuous. For more results, one can refer to [23,25,28,32,33] and references therein.…”