ANZIAM  J.  45 (2003), 115-131
Existence of optimal controls for semilinear elliptic equations without Cesari-type conditions

Hongwei Lou
  Mathematical Department
  Fudan University
  Shanghai 200433

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.
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