A class of elliptic quasi-variational-hemivariational inequalities with applications

Abstract: In this paper we study a class of quasi--variational--hemi-va-ria-tio-nal inequalities in reflexive Banach spaces. The inequalities contain a convex potential, a locally Lipschitz superpotential, and a solution-dependent set of constraints. Solution existence and compactness of the solution set to the inequality problem are established based on the Kakutani--Ky Fan--Glicksberg fixed point theorem. Two examples of the interior and boundary semipermeability models illustrate the applicability of our results.