Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896714 | Journal of Functional Analysis | 2018 | 43 Pages |
Abstract
This paper is concerned with the quantitative homogenization of 2m-order elliptic systems with bounded measurable, rapidly oscillating periodic coefficients. We establish the sharp O(ε) convergence rate in Wmâ1,p0 with p0=2ddâ1 in a bounded Lipschitz domain in Rd as well as the uniform large-scale interior Cmâ1,1 estimate. With additional smoothness assumptions, the uniform interior Cmâ1,1, Wm,p and Cmâ1,α estimates are also obtained. As applications of the regularity estimates, we establish asymptotic expansions for fundamental solutions.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Weisheng Niu, Zhongwei Shen, Yao Xu,