Optimality conditions and adjoint state for a perturbed boundary optimal control system

In this paper, we are concerned with finding optimal controls for a class of linear boundary optimal control systems associated to a Laplace operator on a regular bounded domain in the n-dimensional Euclidean space. For these systems, in previous works (see [1,2]), we proved existence of the (perturbed) states and optimal controls, and studied their behaviour. The purpose of this paper is to establish the system of optimality conditions, investigate the adjoint states, and prove their strong convergence in some Sobolev spaces. (C) 2001 Elsevier Science Ltd. All rights reserved.