Spectral properties of periodic media in the large coupling limit
Rainer Hempel, Karsten Lienau · Communications in Partial Differential Equations · 1999
We investigate the bandgap structure and the integrated density of states for a class of periodic divergence type operators which, in the simplest case, are given by , acting in . We assume here that ωis an open, connected, periodic subset of and that the complement M ofωdoes not intersect the boundary of the fundamental period cellQ0. Operators of this type occur in simple models for heat conduction or propagation of acoustic waves in a metal with impurities like grains of sand or air bubbles, and in connectiion with photonic crystals. Among other results, we find that Tλ will always have at least one open gap,for λlarge (except for trivial cases).We also establish a connection between the band-gap nstructure of Tλ and the Dirichlet eigenvalue problem on