
Minimax Theory and its Applications 09 (2024), No. 2, 253270 Copyright Heldermann Verlag 2024 Analysis and Control of a General Elliptic QuasivariationalHemivariational Inequality Weimin Han Department of Mathematics, University of Iowa, Iowa City, U.S.A. weiminhan@uiowa.edu Mircea Sofonea Laboratory of Mathematics and Physics, University of Perpignan, Perpignan, France sofonea@univperp.fr We consider a general elliptic quasivariationalhemivariational inequality in real Hilbert spaces for which we provide a solution existence and uniqueness result, a convergent iterative procedure, and a Lipschitz continuous dependence result that we use in order to deduce the existence of a solution to an associated optimal control problem. As an example for applications of the abstract results, we consider a new model of static contact problem which describes the equilibrium of an elastic body with a reactive foundation. The weak formulation of the model is a quasivariationalhemivariational inequality for the displacement field. We present theoretical results on the analysis and control of the contact problem. Keywords: Quasivariationalhemivariational inequality, existence, uniqueness, optimal control, locking material, frictional contact problem, unilateral constraint, weak solution. MSC: 35J87, 47J20, 49J21, 74M10, 74M15. [ Fulltextpdf (148 KB)] for subscribers only. 