Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form

Scott Armstrong, Charles K. Smart

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)867-911
Number of pages45
JournalArchive for Rational Mechanics and Analysis
Volume214
Issue number3
DOIs
StatePublished - Oct 17 2014

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Stochastic Homogenization
Regularity Theory
Linear equations
Length Scale
Elliptic Equations
Error Estimates
Linear equation
Deviation
Directly proportional
Range of data
Form

ASJC Scopus subject areas

  • Analysis
  • Mechanical Engineering
  • Mathematics (miscellaneous)

Cite this

Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form. / Armstrong, Scott; Smart, Charles K.

In: Archive for Rational Mechanics and Analysis, Vol. 214, No. 3, 17.10.2014, p. 867-911.

Research output: Contribution to journalArticle

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