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arXiv · 1507.06046

Uniform Regularity Estimates in Homogenization Theory of Elliptic Systems with Lower Order Terms on the Neumann Boundary Problem

Qiang Xu
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Abstract

In this paper, we mainly employed the idea of the previous paper to study the sharp uniform $W^{1,p}$ estimates with $1<p\leq \infty$ for more general elliptic systems with the Neumann boundary condition on a bounded $C^{1,\eta}$ domain, arising in homogenization theory. Based on the skills developed by Z. Shen and by T. Suslina for different purposes, we also established the $L^2$ convergence rates on a bounded $C^{1,1}$ domain and a Lipschitz domain, respectively. Here we found a "rough" version of the first order correctors (see Theorem 1.3), It allows us to skip the corresponding convergence results on $\mathbb{R}^d$ that are the preconditions in T. Suslina's papers.

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Qiang Xu. 2015-07-22. Uniform Regularity Estimates in Homogenization Theory of Elliptic Systems with Lower Order Terms on the Neumann Boundary Problem. https://arxiv.org/abs/1507.06046

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