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 C 1, 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 H¨older continuity is the main assumption on smoothness of the data.

中文翻译：

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具有 Dini 条件的散度形式椭圆系统均质化的统一 Lipschitz 估计

该论文致力于椭圆系统在发散形式中的均质化。当系数为 Dini 连续、非齐次项是 Dini 连续函数的发散且边界函数具有 Dini 连续导数时，我们在有界 C 1, γ 域中获得均匀的内部和边界 Lipschitz 估计。结果扩展了 Avellaneda 和 Lin 的工作 [Comm. 纯应用 Math., 40: 803–847 (1987)]，其中 H¨older 连续性是数据平滑度的主要假设。