The periodic unfolding method in perforated domains

The periodic unfolding method was introduced in [4] by D. Cioranescu, A. Damlamian and G. Griso for the study of classical periodic homogenization. The main tools are the unfolding operator and a macro-micro decomposition of functions which allows to separate the macroscopic and microscopic scales.In this paper, we extend this method to the homogenization in domains with holes,introducing the unfolding operator for functions defined on periodically perforated domains as well as a boundary unfolding operator. As an application, we study the homogenization of some elliptic problems with a Robin condition on the boundary of the holes, proving convergence and corrector results.