Uniform regularity estimates in homogenization theory of elliptic systems with lower order terms on the Neumann boundary problem

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Xu, Qiang¹ 

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

关键词: Elliptic systems;    Homogenization;    Uniform regularity estimates;    Neumann boundary problem;    Convergence rates;   

DOI  :  10.1016/j.jde.2016.06.027

来源: Elsevier

【 摘 要 】

In this paper, we mainly employed the idea of the previous paper [34] to study the sharp uniform W-1,W-p estimates with 1 < p <= infinity for more general elliptic systems with the Neumann boundary condition on a bounded C-1,C-eta domain, arising in homogenization theory. Based on the skills developed by Z. Shen in [27] and by T. Suslina in [31,32], we also established the L-2 convergence rates on a bounded C-1,C-1 domain and a Lipschitz domain, respectively. Here we found a rough version of the first order correctors (see (1.12)), which can unify the proof in [27] and [32]. It allows us to skip the corresponding convergence results on R-d that are the preconditions in [31,32]. Our results can be regarded as an extension of [23] developed by C. Kenig, F. Lin, Z. Shen, as well as of [32] investigated by T. Suslina. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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