ANZIAM  J.  44 (2003), 539-559
Minimax control of an elliptic variational bilateral problem

Qihong Chen
  Department of Applied Mathematics
  Shanghai University of Finance and Economics
  777 Guoding Road
  Shanghai 200433
  P. R. China

This paper deals with a minimax control problem for semilinear elliptic variational inequalities associated with bilateral constraints. The control domain is not necessarily convex. The cost functional, which is to be minimised, is the sup norm of some function of the state and the control. The major novelty of such a problem lies in the simultaneous presence of the nonsmooth state equation (variational inequality) and the nonsmooth cost functional (the sup norm). In this paper, the existence conditions and the Pontryagin-type necessary conditions for optimal controls are established.
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