Weighted L2 Estimates for Elliptic Homogenization in Lipschitz Domains

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We develop a new real-variable method for weighted Lp estimates. The method is applied to the study of weighted W1 , 2 estimates in Lipschitz domains for weak solutions of second-order elliptic systems in divergence form with bounded measurable coefficients. It produces a necessary and sufficient condition, which depends on the weight function, for the weighted W1 , 2 estimate to hold in a fixed Lipschitz domain with a given weight. Using this condition, for elliptic systems in Lipschitz domains with rapidly oscillating, periodic and VMO coefficients, we reduce the problem of weighted estimates to the case of constant coefficients.

Original languageEnglish
Article number3
JournalJournal of Geometric Analysis
Issue number1
StatePublished - Jan 2023

Bibliographical note

Funding Information:
This study was supported in part by NSF Grant DMS-1856235.

Publisher Copyright:
© 2022, Mathematica Josephina, Inc.


  • homogenization
  • Lipschitz domain
  • Weighted estimate

ASJC Scopus subject areas

  • Geometry and Topology


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