Maximum principle in optimal control problems for elliptic equations (Q1079802)

Problems of optimal control for quasilinear elliptic differential equations of second order with integral constraints are considered. The main emphasis is on those cases with non-convex sets of admissible controls where all coefficients of the state equation depend on the controls. Necessary optimality conditions in a form of a maximum principle are derived under assumptions analogous to those under which the linearized maximum principle holds in the case of convex sets of admissible controls.