This paper is concerned with the large-scale regularity in the homogenization of elliptic systems of elasticity with periodic high-contrast coefficients. We obtain the large-scale Lipschitz estimate that is uniform with respect to the contrast ratio $\delta^2$ for $0<\delta<\infty$. Our study also covers the case of soft inclusions ($\delta=0$) as well as the case of stiff inclusions ($\delta=\infty$). The large-scale Lipschitz estimate, together with classical local estimates, allows us to establish explicit bounds for the matrix of fundamental solutions and its derivatives.

中文翻译：

---

具有周期性高对比度系数的椭圆系统的大规模 Lipschitz 估计

本文关注具有周期性高对比度系数的椭圆弹性系统均匀化的大尺度规律。我们获得了关于 $0<\delta<\infty$ 的对比度 $\delta^2$ 的大规模 Lipschitz 估计。我们的研究还涵盖了软夹杂物 ($\delta=0$) 以及硬夹杂物 ($\delta=\infty$) 的情况。大规模的 Lipschitz 估计与经典的局部估计一起使我们能够为基本解及其导数的矩阵建立明确的界限。