Existence and uniqueness of a solutions of nonlinear degenerated equations with measure data

Abstract

This paper is devoted to the study of the following of nonlinear degenerate equations of the
type
(P )

Au u = = 0 µ on in Ω@Ω;

where A is a Leray Lions operator acted from weighted Sobolev space W01;p(Ω; !) into its dual
W -1;p0(Ω; !∗), and µ is a Radon measure does not charge the sets of null (p; !)-capacity. We
prove a decomposition theorem for measure does not charge the sets of null (p; !)-capacity. We
apply this result to prove existence and uniqueness of an entropy solution of problem (P ).