Large-scale Lipschitz estimates for elliptic systems with periodic high-contrast coefficients

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 (Formula presented.) for (Formula presented.) Our study also covers the case of soft inclusions (δ = 0) as well as the case of stiff inclusions ((Formula presented.)). 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.