Large-Scale Lipschitz Estimates for Elliptic Systems with Periodic High-Contrast Coefficients

Abstract

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.

28 pages

References in corpus (2)

• Elliptic regularity and quantitative homogenization on percolation clusters
• Large-scale analyticity and unique continuation for periodic elliptic equations