ABSENCE OF GAPS IN A LOWER PART OF THE SPECTRUM OF A LAPLACIAN WITH FREQUENT ALTERNATION OF BOUNDARY CONDITIONS IN A STRIP

被引：2

作者：

Borisov, D. I. ^{[1
,2
,3
]}

机构：

[1] RAS, Ufa Sci Ctr, Inst Math, Comp Ctr, Ufa, Russia

[2] Akhmulla Bashkir State Pedag Univ, Ufa, Russia

[3] Univ Hradec Kralove, Hradec Kralove, Czech Republic

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2018年 / 195卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

Bethe-Sommerfeld conjecture; gap; periodic operator; alternation of boundary conditions; Laplacian; infinite strip; BETHE-SOMMERFELD CONJECTURE; NORM-RESOLVENT CONVERGENCE; DENSITY-OF-STATES; SCHRODINGER OPERATOR; ELLIPTIC-OPERATORS; HOMOGENIZATION; CURVE;

D O I：

10.1134/S0040577918050057

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：690 / 703

页数：14

共 17 条

[1] Absence of Gaps in a Lower Part of the Spectrum of a Laplacian with Frequent Alternation of Boundary Conditions in a Strip
D. I. Borisov
Theoretical and Mathematical Physics, 2018, 195 : 690 - 703
[2] Gaps in the Spectrum of the Laplacian in a Strip with Periodic Delta Interaction
D. I. Borisov
Proceedings of the Steklov Institute of Mathematics, 2019, 305 : S16 - S23
[3] Gaps in the Spectrum of the Laplacian in a Strip with Periodic Delta Interaction
Borisov, D. I.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2019, 305 (Suppl 1) : S16 - S23
[4] SPECTRUM OF THE LAPLACIAN IN A NARROW CURVED STRIP WITH COMBINED DIRICHLET AND NEUMANN BOUNDARY CONDITIONS
Krejcirik, David
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2009, 15 (03): : 555 - 568
[5] On the spectrum of the Laplacian with frequently alternating boundary conditions
Borisov, DI
Gadyl'shin, RR
THEORETICAL AND MATHEMATICAL PHYSICS, 1999, 118 (03) : 272 - 277
[6] On the spectrum of the Laplacian with frequently alternating boundary conditions
D. I. Borisov
R. R. Gadyl’shin
Theoretical and Mathematical Physics, 1999, 118 : 272 - 277
[7] On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets
Borisov D.I.
Computational Mathematics and Mathematical Physics, 2006, 46 (2) : 271 - 281
[8] ON RESOLVENT OF MULTI-DIMENSIONAL OPERATORS WITH FREQUENT ALTERNATION OF BOUNDARY CONDITIONS: CRITICAL CASE
Sharapov, T. F.
UFA MATHEMATICAL JOURNAL, 2016, 8 (02): : 65 - 94
[9] Spectrum of the Laplacian with mixed boundary conditions in a chamfered quarter of layer
Chesnel, Lucas
Nazarov, Sergei A.
Taskinen, Jari
JOURNAL OF SPECTRAL THEORY, 2024, 14 (01) : 37 - 57
[10] On Lacunas in the Lower Part of the Spectrum of the Periodic Magnetic Operator in a Strip
Borisov D.I.
Journal of Mathematical Sciences, 2021, 253 (5) : 599 - 617

← 1 2 →