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A Hardy inequality in twisted waveguides

Ekholm, Tomas LU ; Kovarik, H and Krejcirik, D (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.
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author
organization
publishing date
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
2008-09-02 16:29:15
date last changed
2017-05-14 03:39:29
@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},
  volume       = {188},
  year         = {2008},
}