Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited

Scott Armstrong, Charles K. Smart

Research output: Contribution to journalArticle

Abstract

We give a simplified presentation of the obstacle problem approach to stochastic homogenization for elliptic equations in nondivergence form. Our argument also applies to equations which depend on the gradient of the unknown function. In the latter case, we overcome difficulties caused by a lack of estimates for the first derivatives of approximate correctors by modifying the perturbed test function argument to take advantage of the spreading of the contact set.

Original languageEnglish (US)
Pages (from-to)967-980
Number of pages14
JournalCalculus of Variations and Partial Differential Equations
Volume50
Issue number3
DOIs
StatePublished - 2014

Fingerprint

Stochastic Homogenization
Fully Nonlinear
Elliptic Equations
Obstacle Problem
Corrector
Test function
Contact
Gradient
Derivatives
Derivative
Unknown
Estimate

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited. / Armstrong, Scott; Smart, Charles K.

In: Calculus of Variations and Partial Differential Equations, Vol. 50, No. 3, 2014, p. 967-980.

Research output: Contribution to journalArticle

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