Homogenization of quadratic convolution energies in periodically perforated domains
Andrea Braides, Andrey Lvovich Piatnitski · Advances in Calculus of Variations · 2020
Abstract We prove a homogenization theorem for quadratic convolution energies defined in perforated domains. The corresponding limit is a Dirichlet-type quadratic energy, whose integrand is defined by a non-local cell-problem formula. The proof relies on an extension theorem from perforated domains belonging to a wide class containing compact periodic perforations.