This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates down to the finest microscopic scale via iteration and rescaling arguments. We also obtain a convergence rate in the $L^2$ space by the reiterated homogenization method.

中文翻译：

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重复同质化中的定量估计

本文研究了具有在多个分离尺度上振荡的周期系数的二阶椭圆系统的均质化的定量估计。我们通过迭代和重新缩放参数建立了大尺度的内部和边界 Lipschitz 估计，直到最精细的微观尺度。我们还通过重复的同质化方法获得了 $L^2$ 空间中的收敛速度。