Corrector estimates for elliptic systems with random periodic coefficients

Peter Bella and Felix Otto

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Submission date: 25. Sep. 2014
Pages: 32
published in: Multiscale modeling and simulation, 14 (2016) 4, p. 1434-1462 
DOI number (of the published article): 10.1137/15M1037147
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Abstract:
We consider an elliptic system of equations on the torus ^d with random coefficients A, that are assumed to be coercive and stationary. Using two different approaches we obtain moment bounds on the gradient of the corrector, independent of the domain size L. In the first approach we use Green function representation. For that we require A to be locally Hölder continuous and distribution of A to satisfy Logarithmic Sobolev inequality. The second method works for non-smooth (possibly discontinuous) coefficients, and it requires that statistics of A satisfies Spectral Gap estimate.