Distributed Control for Cooperative Elliptic Systems Under Conjugation Conditions

Abstract

The cooperative elliptic systems involving Laplace operator defined on bounded, continuous and strictly Lipschitz domains of under conjugation conditions are considered. First, the existence and uniqueness of the state for these systems with Dirichlet and conjugation conditions is proved, then the set of equations and inequalities that characterizes the distributed control of these systems is found. The problem with Neumann conditions is also discussed.