Pointwise two-scale expansion for parabolic equations with random coefficients

• 成果类型: Article
• 署名作者: Gu, Yu; Mourrat, Jean-Christophe
• 署名单位: Stanford University; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0667-z
• 发表日期: 2016
• 页码: 585-618
• 关键词: discrete elliptic-equations; central-limit-theorem; Stochastic Homogenization; random-media; approximation; CONVERGENCE; functionals

摘要

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.