Regularity of solutions of parabolic equations with a double nonlinearity and a weight

Abstract

. We study local regularity of solutions of nonlinear parabolic equations with a double degeneracy and a weight. We impose the condition of p -admissibility on the weight; in particular this allows weights in the Muckenhoupt classes A p . We prove that solutions are locally H¨olderian without any restriction on the sign being constant. We prove a Harnack inequality for nonnegative solutions. We examine the stability of the constants as the parameters in the equation approach the linear case.