Homogenization of random convolution energies in heterogeneous and perforated domains
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 Dirichlettype 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 blowup technique common for local energies, that can be extended to this `asymptoticallylocal' case. As a particular application we derive a homogenization theorem on random perforated domains.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.06832
 Bibcode:
 2019arXiv190906832B
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 doi:10.1112/jlms.12431