Homogenization of quadratic convolution energies in periodically perforated domains

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.

Automated summary

In this article, we prove a homogenization theorem for quadratic convolution energies defined in perforated domains. The limit of the corresponding energy is a Dirichlet-type quadratic energy, whose integrand is defined by a non-local cell-problem formula. The proof relies on an extension theorem that applies to a wide class of domains containing compact periodic perforations.