An Elastic Frictional Contact Problem with Unilateral Constraint

Abstract

We consider a mathematical model which describes the equilibrium of an elastic body in contact with two obstacles. We derive its weak formulation which is in a form of an elliptic quasi-variational inequality for the displacement field. Then, under a smallness assumption, we establish the existence of a unique weak solution to the problem. We also study the dependence of the solution with respect to the data and prove a convergence result. Finally, we consider an optimization problem associated with the contact model for which we prove the existence of a minimizer and a convergence result, as well.