NONLINEAR PARABOLIC EQUATIONS WITH MEASURE DATA

摘要

In this paper we give summability results for the gradients of solutions of nonlinear parabolic equations whose model is u'-div(del u (p-2)del u)=mu on Omega x (0, T), (P) with homogeneous Cauchy-Dirichlet boundary conditions, where p > 1 and mu is a bounded measure on Omega x (0, T). We also study how the summability of the gradient improves if the measure mu is a function in L-m(Omega x (0, T), with m ''small.'' Moreover we give a new proof of the existence of a solution for problem (P). (C) 1997 Academic Press. [References: 25]