Operator-norm convergence estimates for elliptic homogenization problems on periodic singular structures

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For an arbitrary periodic Borel measure μ we prove order O(ε) operator-norm resolvent estimates for the solutions to scalar elliptic problems in L 2(ℝ d, dμ ε) with ε-periodic coefficients, ε > 0. Here, μ ε is the measure obtained by ε-scaling of μ. Our analysis includes the case of a measure absolutely continuous with respect to the standard Lebesgue measure, as well as the case of “singular” periodic structures (or “multistructures”), when μ is supported by lower-dimensional manifolds.

Original languageEnglish
Pages (from-to)558-572
Number of pages15
JournalJournal of Mathematical Sciences N.Y.
Issue number4
Early online date18 Jun 2018
Publication statusPublished - 1 Jul 2018

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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