Convergence of convex sets with gradient constraint - Azevedo, Assis (2004)
Given a bounded open subset of R^N, we study the convergence of a sequence (K_n)_{n\in\N} of closed convex subsets of W_0^{1,p}(Ω) (p\in]1,∞[) with gradient constraint, to a convex set K, in the Mosco sense. A particular case of the problem studied is when K_n={v\in W_0^{1,p}(Ω):: F_n(x,\nabla v(x))<= g_n(x) for a.e. x in Ω}. Some examples of non-convergence are presented. We also present an improvement of a result of existence of a solution of a quasivariational inequality, as an application of this Mosco convergence result.