High order correctors and two-scale expansions in stochastic homogenization

• 成果类型: Article
• 署名作者: Gu, Yu
• 署名单位: Stanford University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0750-0
• 发表日期: 2017
• 页码: 1221-1259
• 关键词: CENTRAL-LIMIT-THEOREM; discrete elliptic-equations; random-coefficients; effective conductance; normal approximation; parabolic equations; quantification; fluctuations; CONVERGENCE; environment

摘要

In this paper, we study high order correctors in stochastic homogenization. We consider elliptic equations in divergence form on , with the random coefficients constructed from i.i.d. random variables. We prove moment bounds on the high order correctors and their gradients under dimensional constraints. It implies the existence of stationary correctors and stationary gradients in high dimensions. As an application, we prove a two-scale expansion of the solutions to the random PDE, which identifies the first and higher order random fluctuations in a strong sense.