ABSTRACT
Variational inequality theory was introduced by Hartman and Stampacchia [100] as a tool for the study of partial differential equations with applications principally drawn from mechanics. A variational inequality is an inequality involving a functional, which has to be solved for all the values of a given variable usually belonging to a convex set. The mathematical theory of variational inequality was initially developed to deal with equilibrium problems, precisely the Signorini problem posed by Signorini in 1959 and solved by Fichera [82]. In that model problem, the functional involved was assumed as the first variation of the involved potential energy, therefore this type of inequality has been given the name, the variational inequality.
