Fibre homogenisation

Shane Cooper, Marcus Waurick

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4 Citations (Scopus)
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In this article we present a novel method for studying the asymptotic behaviour, with order-sharp error estimates, of the resolvents of parameter-dependent operator families. The method is applied to the study of differential equations with rapidly oscillating coefficients in the context of second-order PDE systems and the Maxwell system. This produces a non-standard homogenisation result that is characterised by ‘fibre-wise’ homogenisation of the related Floquet-Bloch PDEs. These fibre-homogenised resolvents are shown to be asymptotically equivalent to a whole class of operator families, including those obtained by standard homogenisation methods.

Original languageEnglish
Pages (from-to)3363-3405
Number of pages43
JournalJournal of Functional Analysis
Issue number11
Early online date21 Mar 2019
Publication statusPublished - 1 Jun 2019


  • fibre homogenisation
  • Maxwell's equations
  • resolvent estimates
  • second-order PDE systems

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