Nonlinear Parabolic Equations with Measure Data

In this paper we give summability results for the gradients of solutions of nonlinear parabolic equations whose model isu′−div(|∇u|p−2 ∇u)=μ on Ω×(0, T), (P)with homogeneous Cauchy–Dirichlet boundary conditions, wherep>1 andμis a bounded measure on Ω×(0, T). We also study how the summability of the gradient improves if the measureμis a function inLm(Ω×(0, T)), withm“small.” Moreover we give a new proof of the existence of a solution for problem (P).