Distributed Control of Systems Governed by a General Class of Quasilinear Elliptic Equations

In this paper we are concerned with optimal control problems governed by a general class of quasilinear elliptic equations. Our aim is to prove existence of solution and derive optimality conditions. In order to deal with this last question, we begin investigating differentiability of state (solution of equation) with respect to the control (second term of equation), obtaining it only in certain cases. A perturbation method is used to treat other cases, As a consequence of the optimality system, regularity of optimal control and state is establised.