Anisotropic parabolic problems with measures data

Abstract

In this work, we prove the existence of a weak solution of an anisotropic parabolic problem with measure data u t + Au + F(u,Du) = and u(0) = 0 with and 0 two Radon bounded measures. The operator A is a Leray-Lions operator with anisotropic growth conditions. Our approach is based on the anisotropic Sobolev inequality, a regularity result, a compactness result, and an integration by parts formula.