Bilateral obstacle optimal control for a quasilinear elliptic variational inequality with a source term

In this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality with a source term and the control functions are the upper and the lower obstacles. We assume that the obstacles φ and ψ are in W2,2(Ω), but this causes difficulty for deriving the optimality condition. By applying the weak convergence method, we establish existence and incomplete necessary conditions for the optimal control.