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Homogenization of quadratic convolution energies in periodically perforated domains

Andrea Braides ORCID logo EMAIL logo and Andrey Piatnitski ORCID logo

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.


Communicated by Irene Fonseca


Award Identifier / Grant number: E83C18000100006

Funding statement: The authors acknowledge the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.

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Received: 2019-09-28
Revised: 2020-06-04
Accepted: 2020-06-22
Published Online: 2020-07-16
Published in Print: 2022-07-01

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