Homogenization in perforated domains and interior Lipschitz estimates

B. Chase Russell

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We establish interior Lipschitz estimates at the macroscopic scale for solutions to systems of linear elasticity with rapidly oscillating periodic coefficients and mixed boundary conditions in domains periodically perforated at a microscopic scale ε by establishing H1-convergence rates for such solutions. The interior estimates are derived directly without the use of compactness via an argument presented in [3] that was adapted for elliptic equations in [2] and [11]. As a consequence, we derive a Liouville type estimate for solutions to the systems of linear elasticity in unbounded periodically perforated domains.

Original languageEnglish (US)
Pages (from-to)3396-3418
Number of pages23
JournalJournal of Differential Equations
Issue number6
StatePublished - Sep 15 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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