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 03 Sep 2021


Accepted Paper

Inserted: 15 sep 2019
Last Updated: 3 sep 2021

Journal: J.London Math Soc.
Volume: 104
Pages: 295-319
Year: 2021
Doi: 10.1112/jlms.12431

ArXiv: 1909.06832 PDF


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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