Some optimality conditions of quasilinear elliptic obstacle optimal control problems

This paper is concerned with an obstacle optimal control problem for a quasilinear elliptic variational inequality with a source term. The pth power of Laplacian of the obstacle appears in the cost functional. This feature leads that it is hard to derive the optimality system for the underlying problem. The existence for the optimal control is proved and we also show how to obtain optimality system using a passage to the limit in the approximation process.