Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

Jun Geng, Zhongwei Shen, Liang Song

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, arXiv:1505.00694v2).

Original languageEnglish
Pages (from-to)1205-1236
Number of pages32
JournalArchive for Rational Mechanics and Analysis
Volume224
Issue number3
DOIs
StatePublished - Jun 1 2017

Bibliographical note

Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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