ON THE EXISTENCE OF OPTIMAL CONTROL FOR SEMILINEAR ELLIPTIC EQUATIONS WITH NONLINEAR NEUMANN BOUNDARY CONDITIONS

摘要

An optimal control problem governed by a class of semilinear elliptic equations with nonlinear Neumann boundary conditions is studied in this paper. It is pointed out that the cost functional considered may not be convex. Using a relaxation method, some existence results of an optimal control are obtained.