Anisotropic singular perturbations of variational inequalities

Abstract

We consider variational inequalities involving the p-Laplace operator with anisotropic singular perturbations where the convex set, on which the problem is defined, is also subject to perturbations. This leads to introduce a new convergence of sets, in some suitable sense, conceived from the Mosco convergence and matching well to the anisotropic singular perturbations. Convergence results and their rates are established. In order to illustrate the introduced convergence sets, obstacle and elasto-plastic perturbed problems are dealt with. This allows to go deeper in the analysis of the suggested convergence on concrete sets in Sobolev spaces.