Existence of optimal controls for semilinear elliptic equations without Cesari-type conditions

Abstract

Optimal control problems governed by semilinear elliptic partial differential equations are considered. No Cesari-type conditions are assumed. By proving an existence theorem and the Pontryagin maximum principle of optimal "state-control" pairs for the corresponding relaxed problems, we establish an existence theorem of optimal pairs for the original problem. © Australian Mathematical Society 2003.