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

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4 Scopus citations


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.

Original languageEnglish
Pages (from-to)1027-1057
Number of pages31
JournalCommunications in Partial Differential Equations
Issue number6
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.


  • 35B27
  • 74Q05
  • High-contrast coefficient
  • large-scale estimate
  • perforated domains

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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