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

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 φφ and ψψ are in W2,2(Ω)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.