Elliptic Variational Inequalities

In this chapter, we present some theorems on the solvability of elliptic variational and quasivariational inequalities. We start with a basic existence and uniqueness result for elliptic variational inequalities, then we provide convergence results. Next, we extend part of these results to the study of elliptic quasivariational and time-dependent variational and quasivariational inequalities, respectively. The results presented in this chapter will be applied in the study of static antiplane frictional contact problems with elastic materials. They also are crucial tools in deriving existence results for evolutionary variational inequalities. Everywhere in this chapter, X denotes a real Hilbert space with inner product (·,·)X and norm $||\cdot||\ X$.