EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTIONS FOR NONLINEAR ELLIPTIC-EQUATIONS WITH MEASURE DATA

We consider the differential problem {A(u) = mu in Omega, u = 0 on par tial derivative Omega, () where Omega is a bounded, open subset of R( N), N greater than or equal to 2, A is a monotone operator acting on W -0(1,p)(Omega), p > 1, and mu is a Radon measure on Omega that does no t charge the sets of zero p-capacity. We prove a decomposition theorem for these measures (more precisely, as the sum of a function in L(1)( Omega) and of a measure in W--1,W-p'(Omega)), and an existence and uni queness result for the so-called entropy solutions of ().