MOSCO-CONVERGENCE OF CONVEX SETS AND UNILATERAL PROBLEMS FOR DIFFERENTIAL OPERATORS WITH LOWER ORDER TERMS HAVING NATURAL GROWTH

We study the stability of solutions to a class of variational inequalities posed on obstacle-type convex sets, under Mosco-convergence. Specifically, we consider problems of the form { u is an element of W-0(1,p) (ohm) boolean AND L-infinity(ohm), u >= psi in ohm, < A(u), v - u > + integral(ohm) H(x, u, Du) (v - u) >= 0, for all v is an element of W-0(1,p) (ohm) boolean AND L-infinity(ohm), v >= psi in ohm. Here, Ais a Leray-Lions type operator, mapping W-0(1,p)(ohm) into its dual W--1,W-p '(ohm), while H(x, u, Du) grows like |Du|(p). The obstacle psi is a function in W-0(1,p)(ohm) boolean AND L-infinity(ohm). Our main result establishes that the solutions are stable under Mosco-convergence of the constraint sets. This extends classical stability results to natural growth problems.