Calculus of Variations and Geometric Measure Theory
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A. Braides - A. Piatnitski

Homogenization of random convolution energies

created by braidesa on 15 Sep 2019
modified on 06 Jan 2021

[BibTeX]

Accepted Paper

Inserted: 15 sep 2019
Last Updated: 6 jan 2021

Journal: J.London Math Soc.
Year: 2020
Doi: 10.1112/jlms.12431

ArXiv: 1909.06832 PDF

Abstract:

We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity we prove that the $\Gamma$-limit of such energy is almost surely a deterministic quadratic Dirichlet-type integral functional, whose integrand can be characterized through an asymptotic formula. The proof of this characterization relies on results on the asymptotic behaviour of subadditive processes. The proof of the limit theorem uses a blow-up technique common for local energies, that can be extended to this `asymptotically-local' case. As a particular application we derive a homogenization theorem on random perforated domains.


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