Combined effects of homogenization and singular perturbations: Quantitative estimates

Weisheng Niu, Zhongwei Shen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We investigate quantitative estimates in periodic homogenization of second-order elliptic systems of elasticity with singular fourth-order perturbations. The convergence rates, which depend on the scale κ that represents the strength of the singular perturbation and on the length scale ϵ of the heterogeneities, are established. We also obtain the large-scale Lipschitz estimate, down to the scale ϵ and independent of κ. This large-scale estimate, when combined with small-scale estimates, yields the classical Lipschitz estimate that is uniform in both ϵ and κ.

Original languageEnglish
Pages (from-to)351-384
Number of pages34
JournalAsymptotic Analysis
Issue number3
StatePublished - 2022

Bibliographical note

Funding Information:
W. Niu supported by the NSF of China (11971031, 11701002). Z. Shen supported in part by NSF grant DMS-1856235.

Publisher Copyright:
© 2022 - IOS Press. All rights reserved.


  • convergence rate
  • Homogenization
  • singular perturbation
  • uniform Lipschitz estimate

ASJC Scopus subject areas

  • Mathematics (all)


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