Penalty and regularization method for variational-hemivariational inequalities with application to frictional contact

In this paper, we provide results on existence, uniqueness and convergence for a class of variational-hemivariational inequalities of elliptic type involving a constraint set and a nondifferentiable potential. We introduce a penalized and regularized problem without constraints and with Gateaux differentiable potential. We prove that the solution to the original problem can be approached, as a parameter converges, by the solution of the approximated problem. An application to frictional contact problem with the Signorini contact condition and a static version of the Coulomb friction law illustrates the results.