Quantitative stochastic homogenization of elliptic equations in nondivergence form
Analysis of PDEs
2019-12-10 v5 Probability
Abstract
We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional to a power of the microscopic length scale, assuming a finite range of dependence. The results are new even for linear equations. The arguments rely on a new geometric quantity which is controlled in part by adapting elements of the regularity theory for the Monge-Amp\`ere equation.
Keywords
Cite
@article{arxiv.1306.5340,
title = {Quantitative stochastic homogenization of elliptic equations in nondivergence form},
author = {Scott N. Armstrong and Charles K. Smart},
journal= {arXiv preprint arXiv:1306.5340},
year = {2019}
}
Comments
40 pages. This version correctors some minor mistakes in the published version of the article, which are described in Section 1.5. Compared to v4, a typo has been fixed in (4.4) and (4.5)