Abstract Following a framework initiated by Blanc, Le Bris and Lions, this article aims at obtaining quantitative homogenization results in a simple case of interface between two periodic media. By using Avellaneda and Lin’s techniques, we provide pointwise estimates for the gradient of the solution to the multiscale problem and for the associated Green function. Also we generalize the classical two-scale expansion in order to build a pointwise approximation of the gradient of the solution to the multiscale problem (up to the interface), and, adapting Kenig, Lin and Shen’s approach, we obtain convergence rates.

中文翻译：

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一些定量的均质化导致界面的简单情况

摘要 遵循Blanc、Le Bris 和Lions 发起的框架，本文旨在在两种周期介质之间的简单界面情况下获得定量的均质化结果。通过使用 Avellaneda 和 Lin 的技术，我们提供了多尺度问题解的梯度和相关格林函数的逐点估计。我们还推广了经典的两尺度扩展，以建立多尺度问题（直到界面）解的梯度的逐点近似，并且，采用 Kenig、Lin 和 Shen 的方法，我们获得收敛率。