Optimal control of bilateral obstacle problems

摘要

We consider an optimal control problem where the state satisfies a bilateral elliptic variational inequality and the control functions are the upper and lower obstacles. We seek a state that is close to a desired pro. le and the H-2 norms of the obstacles are not too large. Existence results are given and an optimality system is derived. A particular case is studied that needs no compactness assumption, via a monotonicity method.