Uniform regularity estimates in homogenization theory of elliptic system with lower order terms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:438

Article

Xu, Qiang¹ 

[1] Lanzhou Univ, Dept Math, Lanzhou 730000, Peoples R China

关键词: Elliptic systems;    Homogenization;    Uniform regularity estimates;    Green's matrix;   

DOI  :  10.1016/j.jmaa.2016.02.011

来源: Elsevier

【 摘 要 】

In this paper, we extend the uniform regularity estimates obtained by M. Avellaneda and F. Lin in [3,6] to the more general second order elliptic systems in divergence form {L-epsilon,epsilon > 0}, with rapidly oscillating periodic coefficients. We establish not only sharp W-1,W-p estimates, Holder estimates, Lipschitz estimates and non-tangential maximal function estimates for the Dirichlet problem on a bounded C-1,C-n domain, but also a sharp O(epsilon) convergence rate in H-0(1) (Omega) by virtue of the Dirichlet correctors. Moreover, we define the Green's matrix associated with L-epsilon and obtain its decay estimates. We remark that the well known compactness methods are not employed here, instead we construct the transformations (1.11) to make full use of the results in [3,6]. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free