Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form
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205_2014_Article_765.pdf
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Author(s)
Armstrong, Scott N.
Smart, Charles
Date Issued
June 2014
Journal
Archive for Rational Mechanics and Analysis
Publisher
Springer Berlin Heidelberg
Citation
Armstrong, Scott N., and Charles K. Smart. “Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form.” Archive for Rational Mechanics and Analysis 214.3 (2014): 867–911.
Version
Author's final manuscript
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–Ampère equation.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00205-014-0765-6
