We investigate Lamé systems in periodically perforated domains, and establish quantitative homogenization results in the setting where the domain is clamped at the boundary of the holes. Our method is based on layer potentials and it provides a unified proof for various regimes of hole-cell ratios (the ratio between the size of the holes and the size of the periodic cells), and, more importantly, it yields natural correctors that facilitate error estimates. A key ingredient is the asymptotic analysis for the rescaled cell problems, and this is studied by exploring the convergence of the periodic layer potentials for the Lamé system to those in the whole space when the period tends to infinity.

我们研究周期性穿孔区域中的Lamé系统，并在区域被夹持在孔边界处的设置中建立定量均质化结果。我们的方法基于层电势，它为各种孔-细胞比率（孔的大小与周期细胞的大小之间的比率）提供了统一的证明，更重要的是，它产生了自然校正剂，有助于误差估计。关键因素是重新定标的细胞问题的渐近分析，这是通过探索当周期趋于无穷大时Lamé系统的周期层电势与整个空间中的电势的收敛性而进行研究的。