JournalsjstVol. 7, No. 4pp. 1171–1233

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

  • Minh Kha

    Texas A&M University, College Station, USA
  • Peter Kuchment

    Texas A&M University, College Station, USA
  • Andrew Raich

    University of Arkansas, Fayetteville, USA
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior cover
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Abstract

Precise asymptotics known for the Green function of the Laplacian have found their analogs for bounded below periodic elliptic operators of the second-order below and at 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. In a previous work, two of the authors considered the case of a spectral edge. The main result of this article is nding such asymptotics near a gap edge, for “generic” periodic elliptic operators of second-order with real coecients in dimension d2d ≥ 2, when the gap edge occurs at a symmetry point of the Brillouin zone.

Cite this article

Minh Kha, Peter Kuchment, Andrew Raich, Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior. J. Spectr. Theory 7 (2017), no. 4, pp. 1171–1233

DOI 10.4171/JST/188