Large-scale Lipschitz estimates for elliptic systems with periodic high-contrast coefficients
Zhongwei Shen · Communications in Partial Differential Equations · 2020
This article 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 δ2 for 0<δ<∞. Our study also covers the case of soft inclusions (δ = 0) as well as the case of stiff inclusions (δ=∞). 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.