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The aim of this paper is to study the limiting behavior of solutions of a class of optimal control problems governed by elliptic boundary value problems on perforated domains. It is assumed that the coefficients of the differential operator in the state equation and those occurring in the Dirichlet-type integral of the state variable in the cost functional are rapidly oscillating. ᮊ 1999 Academic Press M m Ž . constants. We denote by M M ␣ , ␣ , ⍀ the set of all n = n matrices m M Ž . A s a whose entries are functions on ⍀ such that i j
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