Abstract
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 when the dimension d ≥ 3. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Original language | English (US) |
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Pages (from-to) | 1880-1894 |
Number of pages | 15 |
Journal | Mathematische Nachrichten |
Volume | 285 |
Issue number | 14-15 |
DOIs | |
State | Published - Jun 21 2012 |
Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: P. 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.