We investigate quantitative estimates in periodic homogenization of second-order elliptic systems of elasticity with singular fourth-order perturbations. The convergence rates, which depend on the scale κ that represents the strength of the singular perturbation and on the length scale ε of the heterogeneities, are established. We also obtain the large-scale Lipschitz estimate, down to the scale ε and independent of κ. This large-scale estimate, when combined with small-scale estimates, yields the classical Lipschitz estimate that is uniform in both ε and κ.

中文翻译：

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同质化和奇异扰动的综合影响：定量估计

我们研究了具有奇异四阶扰动的二阶椭圆弹性系统的周期性均匀化的定量估计。收敛速度取决于表示奇异扰动强度的尺度 κ 和异质性的长度尺度 ε。我们还获得了大规模的 Lipschitz 估计，直到尺度 ε 并且与 κ 无关。这种大规模估计与小规模估计相结合时，会产生在 ε 和 κ 中均一的经典 Lipschitz 估计。