Boundary Layers in Periodic Homogenization of Neumann Problems

Zhongwei Shen, Jinping Zhuge

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


This paper is concerned with a family of second-order elliptic systems in divergence form with rapidly oscillating periodic coefficients. We initiate the study of homogenization and boundary layers for Neumann problems with first-order oscillating boundary data. We identify the homogenized system and establish the sharp rate of convergence in L2 in dimension three or higher. Regularity estimates are also obtained for the homogenized boundary data in both Dirichlet and Neumann problems. The results are used to establish a higher-order convergence rate for Neumann problems with nonoscillating data.

Original languageEnglish
Pages (from-to)2163-2219
Number of pages57
JournalCommunications on Pure and Applied Mathematics
Issue number11
StatePublished - Nov 2018

Bibliographical note

Funding Information:
Acknowledgment. Zhongwei Shen is supported in part by National Science Foundation Grant DMS-1600520. Jinping Zhuge is supported in part by National Science Foundation Grant DMS-1161154. Zhongwei Shen thanks David Gérard-Varet for bringing the problem of homogenization of the Neumann problem (1.1) to his attention.

Publisher Copyright:
© 2018 Wiley Periodicals, Inc.

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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