ABSTRACT
The notion of hemivariational inequalities was introduced in the 1980s by P.D. Panagiotopoulos (see [13-15]). These new expressions are a natural extension of variational inequalities. They arise in physical problems when we deal with nonsmooth and nonconvex potential functionals and thus with nonmonotone and possibly multivalued laws. Such functionals appear quite often in mechanics and engineering if one wants
to consider more realistic mechanical laws of nonmonotone, multivalued nature. Hemivariational inequalities use the notion of Clarke’s subdifferential of locally Lipschitz functions (see F.H. Clarke [4]), which is a generalization of classical derivative of smooth functions as well as subdifferential of convex functions in the sense of convex analysis. For particular applications of hemivariational inequalities to problems in mechanics and engineering we refer to the books of P.D. Panagiotopoulos [13, 16], Z. Naniewicz and P.D. Panagiotopoulos [12], and references therein.
