Indirect obstacle minimax control for elliptic variational inequalities (Q1608143)

The paper considers an optimal control problem governed by an elliptic obstacle variational inequality where the obstacle itself is a solution of a semilinear elliptic equation depending on control, too. The cost functional is defined by the sup norm. Assuming the Cesari property the existence of an optimal solution is obtained. By approximating the cost functional with \(L_p\) norms, \(p\to \infty\), optimality conditions for the original problem are derived in the form of Pontryagin's maximum principle with Lagrange multipliers from measure spaces.