TY - JOUR
T1 - Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case
AU - Kuchment, Peter
AU - Raich, Andrew
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged 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.
PY - 2012/6/21
Y1 - 2012/6/21
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/598432
UR - http://doi.wiley.com/10.1002/mana.201100272
UR - http://www.scopus.com/inward/record.url?scp=84867135265&partnerID=8YFLogxK
U2 - 10.1002/mana.201100272
DO - 10.1002/mana.201100272
M3 - Article
SN - 0025-584X
VL - 285
SP - 1880
EP - 1894
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 14-15
ER -