Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case

Details Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case

2011-10-02

arxiv.org/abs/1110.0225v1

Physics

Mathematical Physics

Scientific paper

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.

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