Necessary conditions for boundary control problem governed by variational inequalities with an infinite number of variables

Abstract

In this paper we find the necessary conditions for optimality in boundary control problem governed by variational inequality with an infinite number of variables in the case of the control and observation are on the boundary. First order necessary conditions of the optimality are obtained for the control problem using theorems of Lions [9], Barbu [1], a previous result of Gali et.al. [8] and [5].