Stochastic homogenization of convolution type operators
Functional Analysis
2018-07-19 v2
Abstract
This paper deals with homogenization problem for convolution type non-local operators in random statistically homogeneous ergodic media. Assuming that the convolution kernel has a finite second moment and satisfies the uniform ellipticity and certain symmetry conditions, we prove the almost sure homogenization result and show that the limit operator is a second order elliptic differential operator with constant deterministic coefficients.
Cite
@article{arxiv.1806.00995,
title = {Stochastic homogenization of convolution type operators},
author = {Andrey Piatnitski and Elena Zhizhina},
journal= {arXiv preprint arXiv:1806.00995},
year = {2018}
}