On the spectrum of narrow periodic waveguides

L. Friedlander; M. Solomyak

doi:10.1134/S1061920808020076

On the spectrum of narrow periodic waveguides

L. Friedlander, M. Solomyak

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

This is a continuation of [1] and [2]. We consider the spectrum of the Dirichlet Laplacian on the domain {(x, y) : 0 < y < εh(x)}, where h(x) is a positive periodic function. The main assumption is that h(x) has one point of global maximum on the period interval. We study the location of bands and prove that the band lengths decay exponentially as ε → 0.

Original language	English (US)
Pages (from-to)	238-242
Number of pages	5
Journal	Russian Journal of Mathematical Physics
Volume	15
Issue number	2
DOIs	https://doi.org/10.1134/S1061920808020076
State	Published - Jun 2008

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1134/S1061920808020076

Cite this

@article{5d9b929d0003428797ac96221ef37fb3,

title = "On the spectrum of narrow periodic waveguides",

abstract = "This is a continuation of [1] and [2]. We consider the spectrum of the Dirichlet Laplacian on the domain {(x, y) : 0 < y < εh(x)}, where h(x) is a positive periodic function. The main assumption is that h(x) has one point of global maximum on the period interval. We study the location of bands and prove that the band lengths decay exponentially as ε → 0.",

author = "L. Friedlander and M. Solomyak",

note = "Funding Information: The work was mostly done when both authors visited the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK. We acknowledge the hospitality of the Newton Institute. The first author was partially supported by the NSF grant DMS 0648786.",

year = "2008",

month = jun,

doi = "10.1134/S1061920808020076",

language = "English (US)",

volume = "15",

pages = "238--242",

journal = "Russian Journal of Mathematical Physics",

issn = "1061-9208",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

TY - JOUR

T1 - On the spectrum of narrow periodic waveguides

AU - Friedlander, L.

AU - Solomyak, M.

N1 - Funding Information: The work was mostly done when both authors visited the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK. We acknowledge the hospitality of the Newton Institute. The first author was partially supported by the NSF grant DMS 0648786.

PY - 2008/6

Y1 - 2008/6

N2 - This is a continuation of [1] and [2]. We consider the spectrum of the Dirichlet Laplacian on the domain {(x, y) : 0 < y < εh(x)}, where h(x) is a positive periodic function. The main assumption is that h(x) has one point of global maximum on the period interval. We study the location of bands and prove that the band lengths decay exponentially as ε → 0.

AB - This is a continuation of [1] and [2]. We consider the spectrum of the Dirichlet Laplacian on the domain {(x, y) : 0 < y < εh(x)}, where h(x) is a positive periodic function. The main assumption is that h(x) has one point of global maximum on the period interval. We study the location of bands and prove that the band lengths decay exponentially as ε → 0.

UR - http://www.scopus.com/inward/record.url?scp=45149112159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45149112159&partnerID=8YFLogxK

U2 - 10.1134/S1061920808020076

DO - 10.1134/S1061920808020076

M3 - Article

AN - SCOPUS:45149112159

SN - 1061-9208

VL - 15

SP - 238

EP - 242

JO - Russian Journal of Mathematical Physics

JF - Russian Journal of Mathematical Physics

IS - 2

ER -

On the spectrum of narrow periodic waveguides

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this