Optimal control of unilateral obstacle problem with a source term

TL;DR

This paper addresses the optimal control of an obstacle problem governed by elliptic variational inequalities, introducing an approximation method to establish existence and derive necessary optimality conditions.

Contribution

It presents a novel approximation technique for the obstacle control problem with an obstacle function in H^2, proving existence and deriving optimality conditions.

Findings

Existence of optimal solutions established.

Necessary optimality conditions derived.

Approximate problems governed by variational equations introduced.

Abstract

We consider an optimal control problem for the obstacle problem with an elliptic variational inequality. The obstacle function which is the control function is assumed in $H^{2}$. We use an approximate technique to introduce a family of problems governed by variational equations. We prove optimal solutions existence and give necessary optimality conditions.