ANZIAM J.
44 (2003), 539-559
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Minimax control of an elliptic variational bilateral problem
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Qihong Chen
Department of Applied Mathematics
Shanghai University of Finance and Economics
777 Guoding Road
Shanghai 200433
P. R. China
chenqih@online.sh.cn
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Abstract
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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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