Green's function asymptotics near the internal edges of spectra of   periodic elliptic operators. Spectral edge case
  Precise asymptotics known for the Green's function of the Laplace operator have found their analogs for periodic elliptic operators of the second order at and below the bottom of the spectrum. Due to the band-gap structure of the spectra of such operators, the question arises whether similar results can be obtained near or at the edges of spectral gaps. As the result of this work shows, this is possible at a spectral edge in dimensions d>2. 
Peter Kuchment and Andrew Raich
math-ph math.MP