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

Abstract

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 $0<\delta <\infty .$ Our study also covers the case of soft inclusions (δ = 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.

Keywords:

• High-contrast coefficient
• large-scale estimate
• perforated domains

MR (2020) Subject Classification:

• 35B27
• 74Q05

Additional information

Funding

This study was supported in part by NSF grant DMS-1856235.