Uniform Lipschitz Estimates of Homogenization of Elliptic Systems in Divergence Form with Dini Conditions

• 作者: Rong DONG Dong-sheng LI Hai-liang ZHANG
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 48-68
• 页数: 21页
• 语种: 英文

摘要

The paper is devoted to the homogenization of elliptic systems in divergence form.We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1,γ domain when the coefficients are Dini continuous,inhomogeneous terms are divergence of Dini continuous functions and the boundary functions have Dini continuous derivatives.The results extend Avellaneda and Lin's work[Comm.Pure Appl.Math.,40:803-847(1987)],where Holder continuity is the main assumption on smoothness of the data.