
Optimal quantitative estimates in stochastic homogenization for elliptic equations in nondivergence form
Armstrong, Scott N.; Lin, Jessica (2017), Optimal quantitative estimates in stochastic homogenization for elliptic equations in nondivergence form, Archive for Rational Mechanics and Analysis, 225, 2, p. 937–991. 10.1007/s00205-017-1118-z
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Article accepté pour publication ou publiéDate
2017Journal name
Archive for Rational Mechanics and AnalysisVolume
225Number
2Publisher
Springer
Pages
937–991
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Show full item recordAbstract (EN)
We 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.Subjects / Keywords
stochastic homogenization; correctors; error estimateRelated items
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