Journal
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volume 104, Issue 1, Pages 295-319Publisher
WILEY
DOI: 10.1112/jlms.12431
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Funding
- MIUR Excellence Department Project [CUP E83C18000100006]
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The study establishes a homogenization theorem for a class of quadratic convolution energies with random coefficients, showing that the Gamma-limit of such energy is almost surely a deterministic quadratic Dirichlet-type integral functional. The proof relies on results on the asymptotic behavior of subadditive processes and uses a blow-up technique common for local energies.
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, which 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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