Pointwise two-scale expansion for parabolic equations with random coefficients
Probability
2015-09-17 v3 Analysis of PDEs
Abstract
We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension and higher and for coefficients having a finite range of dependence, we prove a pointwise version of the two-scale expansion. A similar expansion is derived for elliptic equations in divergence form. The result is surprising, since it was not expected to be true without further symmetry assumptions on the law of the coefficients.
Cite
@article{arxiv.1410.2157,
title = {Pointwise two-scale expansion for parabolic equations with random coefficients},
author = {Yu Gu and Jean-Christophe Mourrat},
journal= {arXiv preprint arXiv:1410.2157},
year = {2015}
}
Comments
25 pages. Minor revisions, to appear in PTRF