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 delta(2) for 0 < delta < infinity. Our study also covers the case of soft inclusions (delta = 0) as well as the case of stiff inclusions (delta = infinity). 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.