On the density of states of periodic media in the large coupling limit

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Let Ω0 be a domain in the cube (0, 2π)n, and let χτ(x) be a function that equals 1 inside Ω0, equals τ in (0, 2π)n0, and that is extended periodically to Rn. It is known that, in the limit τ → ∞, the spectrum of the operator - ∇χτ(x)∇ exhibits the band-gap structure. We establish the asymptotic behavior of the density of states function in the bands.

Original languageEnglish (US)
Pages (from-to)355-380
Number of pages26
JournalCommunications in Partial Differential Equations
Issue number1-2
StatePublished - Oct 7 2002


ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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