Optimal Control and Admissible Relaxation of Uncertain Nonlinear Elliptic Systems

In this article we study the optimal control of uncertain systems monitored by nonlinear elliptic equations. First under convexity hypotheses, we show that the min]max problem has a solution. Then we drop the convexity assumptions and we pass to the larger relaxed system. We show that this always has a solution under very general hypotheses on the data. We also produce conditions that guarantee that the relaxation is admissible; i.e., the relaxed problem is the ‘‘closure’’ of the original one. Q 1996 Academic Press, Inc.