Calculus of Variations and Geometric Measure Theory

A. Braides - A. Piatnitski

Homogenization of quadratic convolution energies in periodically perforated domains

created by braidesa on 18 Sep 2019
modified on 02 Sep 2022


Published Paper

Inserted: 18 sep 2019
Last Updated: 2 sep 2022

Journal: Adv. Calc. Var.
Volume: 15
Pages: 351-368
Year: 2022
Doi: 10.1515/acv-2019-0083

ArXiv: 1909.08713 PDF


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.