论文标题
具有周期性高对比度系数的椭圆系统的大规模Lipschitz估计值
Large-Scale Lipschitz Estimates for Elliptic Systems with Periodic High-Contrast Coefficients
论文作者
论文摘要
本文涉及具有周期性高对比度系数的弹性椭圆系统均质化的大规模规律性。我们获得了大规模LIPSCHITZ估计，该估计值相对于对比度$δ^2 $，价格为$ 0 <Δ<\ infty $。我们的研究还涵盖了软包裹物（$δ= 0 $）的情况以及僵硬的夹杂物（$δ= \ infty $）的情况。大规模Lipschitz估计以及经典的本地估计，使我们能够为基本解决方案及其衍生物的矩阵建立明确的界限。
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 $δ^2$ for $0<δ<\infty$. Our study also covers the case of soft inclusions ($δ=0$) as well as the case of stiff inclusions ($δ=\infty$). 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.
