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

TL;DR

This paper investigates a broad class of elliptic quasi-variational-hemivariational inequalities in reflexive Banach spaces, establishing existence and compactness of solutions, with applications demonstrated through models of interior and boundary semipermeability.

Contribution

It introduces a new framework for elliptic quasi-variational-hemivariational inequalities with solution-dependent constraints, proving existence and compactness results.

Findings

Existence of solutions established using fixed point theorems

Solution set is shown to be compact

Applications to interior and boundary semipermeability models

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.