A regularized frictional contact problem with unilateral constraints

We consider a mathematical model which describes the equilibrium of an elastic body in contact with a deformable foundation. We describe the contact model and we establish the existence of a unique weak solution to the problem. Then, we prove the continuous dependence of the solution with respect to the data. Finally, we introduce a sequence of regularized problems depending on a positive parameter for which we study the convergence when the regularization parameter is very small.