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 R_N 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(T_k(u_n))is strongly compact in W₀ ^1,p(ω) and then that (U_n) converges to a distributional solution of the Dirichlet problem with µ as datum.

Keywords:

• Variational inequalities
• measure data
• strong convergence of truncations

AMS:

• 35J85
• 35J60