Nonlinear parabolic equations with measure data

Abstract

In this paper we give summability results for the gradients of solutions of nonlinear parabolic equations whose model is u′ - div(|∇u|p-2 ∇u = μ on Ω × (0, T), (P) with homogeneous Cauchy-Dirichlet boundary conditions, where p > 1 and μ is a bounded measure on Ω × (0, T). We also study how the summability of the gradient improves if the measure μ is a function in Lm(Ω × (0, T)), with m "small." Moreover we give a new proof of the existence of a solution for problem (P). © 1997 Academic Press.