Absence of gaps in a~lower part of the~spectrum of a~Laplacian with frequent alternation of boundary conditions in a~strip
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 2, pp. 225-239
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We consider the Laplacian in a planar infinite straight strip with frequent alternation of boundary conditions. We show that for a sufficiently small alternation period, there are no gaps in a lower part of the spectrum. In terms of certain numbers and functions, we write an explicit upper bound for the period and an expression for the length of the lower part of the spectrum in which the absence of gaps is guaranteed.
Keywords:
Bethe–Sommerfeld conjecture, gap, periodic operator, alternation of boundary conditions, Laplacian, infinite strip.
@article{TMF_2018_195_2_a4,
author = {D.I. Borisov},
title = {Absence of gaps in a~lower part of the~spectrum of {a~Laplacian} with frequent alternation of boundary conditions in a~strip},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {225--239},
publisher = {mathdoc},
volume = {195},
number = {2},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_2_a4/}
}
TY - JOUR AU - D.I. Borisov TI - Absence of gaps in a~lower part of the~spectrum of a~Laplacian with frequent alternation of boundary conditions in a~strip JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2018 SP - 225 EP - 239 VL - 195 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2018_195_2_a4/ LA - ru ID - TMF_2018_195_2_a4 ER -
%0 Journal Article %A D.I. Borisov %T Absence of gaps in a~lower part of the~spectrum of a~Laplacian with frequent alternation of boundary conditions in a~strip %J Teoretičeskaâ i matematičeskaâ fizika %D 2018 %P 225-239 %V 195 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2018_195_2_a4/ %G ru %F TMF_2018_195_2_a4
D.I. Borisov. Absence of gaps in a~lower part of the~spectrum of a~Laplacian with frequent alternation of boundary conditions in a~strip. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 2, pp. 225-239. http://geodesic.mathdoc.fr/item/TMF_2018_195_2_a4/