A review of optimal control problems for elliptic variational and hemivariational inequalities and their asymptotic behaviors

Abstract

We consider a d-dimensional bounded domain Ω which regular boundary consists of the union of three disjoint portions. We study different optimal control problems (distributed, boundary and simultaneous distributed-boundary) for systems governed by elliptic variational inequalities or elliptic hemivariational inequalities. For both cases, we also consider a parameter, like a heat transfer coefficient on a portion of the boundary, which tends to infinity. We prove an existence result for three different optimal control problems, and we show the asymptotic behavior results for the corresponding optimal controls and system states.