History-dependent hemivariational inequalities with applications to Contact Mechanics

In this paper we survey some of our recent results on the existence and uniqueness of solutions to nonconvex and nonsmooth problems which arise in Contact Mechanics. The approach is based on operator subdifferential inclusions and hemivariational inequalities, and focuses on three aspects. First, we report on results on the second order history-dependent subdifferential inclusions and hemivariational inequalities; next, we discuss a class of stationary history-dependent operator inclusions and hemivariational inequalities; finally, we use these abstract results in the study of two viscoelastic contact problems with subdifferential boundary conditions.