Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case
KAUST Grant NumberKUS-C1-016-04
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AbstractPrecise 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 when the dimension d ≥ 3. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
CitationKuchment P, Raich A (2012) Green’s function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case. Math Nachr 285: 1880–1894. Available: http://dx.doi.org/10.1002/mana.201100272.
SponsorsP. K. expresses his thanks to V. Papanicolaou, Y. Pinchover, T. Tsuchida, and the referee for useful discussions and suggestions. The work of P. K. was supported in part by IAMCS through the KAUST Award No. KUS-C1-016-04. The work of A. R. was supported in part by the NSF grant DMS-0855822. The authors express their gratitude to these institutions for the support.