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Abstract

An optimal control problem for semilinear elliptic partial differential equations is considered. The equation is in divergence form with the leading term containing the control. Necessary conditions for optimal controls are established by the method of homogenized spike variation. The key to such a method is to modify the usual spike variational technique by taking into account the homogenization techniques for elliptic equations, together with an idea from the theory of relaxed controls. Problems with state constraints are also discussed by further adding some well-known penalty arguments involving the application of Ekeland's variational principle and finite codimensionality of certain sets.

Journal Title

Siam Journal on Control and Optimization

Volume

48

Issue/Number

4

Publication Date

1-1-2009

Document Type

Article

First Page

2366

Last Page

2387

WOS Identifier

WOS:000270194500014

ISSN

0363-0129

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