Quantitative stochastic homogenization of convex integral functionals

Scott Armstrong, Charles K. Smart

Research output: Contribution to journalArticle

Abstract

We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but sub-optimal) in the size of the error, but optimal in stochastic integrability. As an application, we obtain quenched C0,1 estimates for local minimizers of such energy functionals.

Original languageEnglish (US)
Pages (from-to)423-481
Number of pages59
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume49
Issue number2
StatePublished - 2016

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Stochastic Homogenization
Integral Functionals
Uniformly Convex
Local Minimizer
Random Coefficients
Homogenization
Dirichlet Problem
Integrability
Error Estimates
Energy
Estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Quantitative stochastic homogenization of convex integral functionals. / Armstrong, Scott; Smart, Charles K.

In: Annales Scientifiques de l'Ecole Normale Superieure, Vol. 49, No. 2, 2016, p. 423-481.

Research output: Contribution to journalArticle

Armstrong, Scott ; Smart, Charles K. / Quantitative stochastic homogenization of convex integral functionals. In: Annales Scientifiques de l'Ecole Normale Superieure. 2016 ; Vol. 49, No. 2. pp. 423-481.
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