Asymptotic behavior of elliptic variational inequalities with measure data

Abstract

Give a bounded positive Radon measure µ we study the asymptotic behavior,as n tends to infinity, of the following class of variational inequalities where ωis an open bounded subest of RN and A is a monotone operator of Leray—Lions type acting on the Sobolev space W0 1,p. We prove that the sequence of truncations(Tk(un))is strongly compact in W0 1,p(ω) and then that (Un) converges to a distributional solution of the Dirichlet problem with µ as datum.