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)n/Ω0, 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.
ASJC Scopus subject areas
- Applied Mathematics