Lipschitz Estimates in Almost-Periodic Homogenization

Scott N. Armstrong, Zhongwei Shen

Research output: Contribution to journalArticlepeer-review


We establish uniform Lipschitz estimates for second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients. We give interior estimates as well as estimates up to the boundary in bounded C1,α domains with either Dirichlet or Neumann data. The main results extend those in the periodic setting due to Avellaneda and Lin for interior and Dirichlet boundary estimates and later Kenig, Lin, and Shen for the Neumann boundary conditions. In contrast to these papers, our arguments are constructive (and thus the constants are in principle computable) and the results for the Neumann conditions are new even in the periodic setting, since we can treat nonsymmetric coefficients. We also obtain uniform W1,p estimates.

Original languageEnglish (US)
Pages (from-to)1882-1923
Number of pages42
JournalCommunications on Pure and Applied Mathematics
Issue number10
StatePublished - Oct 1 2016

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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