Abstract : We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension 3 and higher and for coefficients having a finite range of dependence, we prove a pointwise version of the two-scale expansion. A similar expansion is derived for elliptic equations in divergence form. The result is surprising, since it was not expected to be true without further symmetry assumptions on the law of the coefficients.
https://hal-ens-lyon.archives-ouvertes.fr/ensl-01401891
Contributor : Jean-Christophe Mourrat
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Submitted on : Wednesday, November 23, 2016 - 10:32:23 PM
Last modification on : Thursday, January 11, 2018 - 6:12:31 AM
Long-term archiving on : Tuesday, March 21, 2017 - 2:43:07 AM
Yu Gu, Jean-Christophe Mourrat. Pointwise two-scale expansion for parabolic equations with random coefficients. Probability Theory and Related Fields, Springer Verlag, 2016, 166, pp.585 - 618. ⟨10.1007/s00440-015-0667-z⟩. ⟨ensl-01401891⟩
