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hal.structure.identifier
dc.contributor.authorArmstrong, Scott N.*
hal.structure.identifier
dc.contributor.authorLin, Jessica*
dc.date.accessioned2017-11-27T09:55:22Z
dc.date.available2017-11-27T09:55:22Z
dc.date.issued2017
dc.identifier.issn0003-9527
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17051
dc.language.isoenen
dc.subjectstochastic homogenization
dc.subjectcorrectors
dc.subjecterror estimate
dc.subject.ddc515en
dc.titleOptimal quantitative estimates in stochastic homogenization for elliptic equations in nondivergence form
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe prove quantitative estimates for the stochastic homogenization of linear uniformly elliptic equations in nondivergence form. Under strong independence assumptions on the coefficients, we obtain optimal estimates on the subquadratic growth of the correctors with stretched exponential-type bounds in probability. Like the theory of Gloria and Otto for divergence form equations, the arguments rely on nonlinear concentration inequalities combined with certain estimates on the Green's functions and derivative bounds on the correctors. We obtain these analytic estimates by developing a $C^{1,1}$ regularity theory down to microscopic scale, which is of independent interest and is inspired by the~$C^{0,1}$ theory introduced in the divergence form case by the first author and Smart.
dc.relation.isversionofjnlnameArchive for Rational Mechanics and Analysis
dc.relation.isversionofjnlvol225
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages937–991
dc.relation.isversionofdoi10.1007/s00205-017-1118-z
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-15T15:25:59Z
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