We study the limiting behavior of an optimal control problem for a linear elliptic equation subject to control and state constraints. Each constituent of the mathematical description of such an optimal control problem may depend on a small parameter . We study the limit of this problem when in the framework of variational -convergence which generalizes the concept of -convergence. We also introduce the notion of -convergence generalizing the concept of -convergence to operators with constraints. We show convergence of the sequence of optimal control problems and identify its limit. We then apply the theory to an elliptic problem on a perforated domain.
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Peter I. Kogut, Günter Leugering, On -Homogenization of an Optimal Control Problem with Control and State Constraints. Z. Anal. Anwend. 20 (2001), no. 2, pp. 395–429DOI 10.4171/ZAA/1023