A Regularization Method for Quasivariational Inequalities

The present paper deals with new results in the study of a class of elliptic quasivariational inequalities in Hilbert spaces. We present a regularization method which consist to consider a sequence of regularized elliptic quasivariational inequalities and prove a convergence result when the parameter of regularization is very small using arguments of monotonicity, convexity, and lower semicontinuity. The mathematical tools developed in this paper are useful in the analysis of a large class of contact problems which lead, in a weak formulation, to elliptic quasivariational inequalities. To provide an example, we illustrate our results in the study of a nonlinear antiplane problem which models the deformation of an antiplane frictional contact for elastic body. The contact is modeled with the static version of the slip-dependent Coulomb's law.