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Minimax control of an elliptic variational bilateral problem

Published online by Cambridge University Press:  17 February 2009

Qihong Chen
Qihong Chen
Affiliation:
Department of Applied Mathematics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai 200433, P. R. China: e-mail: 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.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 4 , April 2003 , pp. 539 - 559
Copyright
Copyright © Australian Mathematical Society 2003

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