A Hardy inequality in twisted waveguides
(2008) In Archive for Rational Mechanics and Analysis 188(2). p.245-264- Abstract
- We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1185167
- author
- Ekholm, Tomas LU ; Kovarik, H and Krejcirik, D
- organization
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Archive for Rational Mechanics and Analysis
- volume
- 188
- issue
- 2
- pages
- 245 - 264
- publisher
- Springer
- external identifiers
-
- wos:000254176700003
- scopus:41149122006
- ISSN
- 0003-9527
- DOI
- 10.1007/s00205-007-0106-0
- language
- English
- LU publication?
- yes
- id
- d77bcccb-b23e-4fd9-aff2-5c147586682c (old id 1185167)
- date added to LUP
- 2016-04-01 12:25:57
- date last changed
- 2022-01-27 03:38:34
@article{d77bcccb-b23e-4fd9-aff2-5c147586682c,
abstract = {{We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.}},
author = {{Ekholm, Tomas and Kovarik, H and Krejcirik, D}},
issn = {{0003-9527}},
language = {{eng}},
number = {{2}},
pages = {{245--264}},
publisher = {{Springer}},
series = {{Archive for Rational Mechanics and Analysis}},
title = {{A Hardy inequality in twisted waveguides}},
url = {{http://dx.doi.org/10.1007/s00205-007-0106-0}},
doi = {{10.1007/s00205-007-0106-0}},
volume = {{188}},
year = {{2008}},
}