Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited

Scott N. Armstrong; Charles K. Smart

doi:10.1007/s00526-013-0663-z

Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited

Scott N. Armstrong, Charles K. Smart

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	967-980
Number of pages	14
Journal	Calculus of Variations and Partial Differential Equations
Volume	50
Issue number	3
DOIs	https://doi.org/10.1007/s00526-013-0663-z
State	Published - Jun 2014

ASJC Scopus subject areas

Analysis
Applied Mathematics

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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.",

author = "Armstrong, {Scott N.} and Smart, {Charles K.}",

note = "Funding Information: SNA was partially supported by NSF Grant DMS-1004645 and by a Chaire Junior of la Fondation Sciences Math{\'e}matiques de Paris. CKS was partially supported by NSF Grant DMS-1004595.",

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AU - Smart, Charles K.

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PY - 2014/6

Y1 - 2014/6

N2 - 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.

AB - 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.

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JO - Calculus of Variations and Partial Differential Equations

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IS - 3

ER -

Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited

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