The maximum principle in optimal control problems for an elliptic equation (in Russian)

Abstract

Problems of optimal control are considered under state equations in the form of quasilinear second-order elliptic differential equations of divergence type, with equations and inequalities as integral constraints. The main stress is on those cases with non-convex sets of admissible controls where all coefficients of the state equation depend on the controls. A maximum principle in integrated form, embodying necessary conditions for optimality, is derived under assumptions analogous to those under which the linearized maximum principle holds in the ease of convex sets of admissible controls.