Homogenization of optimal control problems in perforated domains via periodic unfolding method

Abstract

This article aims to study the limiting behaviors of optimal control problems based on an elliptic boundary value problem with highly oscillating coefficients in a periodically perforated domain. We consider two different types of cost functionals, the -cost functional and the Dirichlet cost functional. We use the periodic unfolding method for perforated domains to homogenize the problems. Moreover, we prove that under this method, only the energy corresponding to the former cost functional converges.