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Nodal domains in the square – the Neumann case

Helffer, Bernard and Persson Sundqvist, Mikael LU (2015) In Moscow Mathematical Journal 15(3). p.455-495
Abstract
A. Pleijel has proved that in the case of the Laplacian on the square with Neumann condition, the equality in the Courant nodal theorem (Courant sharp situation) can only be true for a finite number of eigenvalues. We identify five Courant sharp eigenvalues for the Neumann Laplacian in the square, and prove that there are no other cases.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Nodal domains, Courant theorem, Square, Neumann
in
Moscow Mathematical Journal
volume
15
issue
3
pages
455 - 495
publisher
Independent University of Moscow
external identifiers
  • wos:000365392600004
  • scopus:84943530258
ISSN
1609-3321
language
English
LU publication?
yes
id
31e252fe-0204-4e69-86fc-50e5d5356f04 (old id 8539801)
date added to LUP
2016-01-20 11:03:52
date last changed
2017-04-23 03:57:21
@article{31e252fe-0204-4e69-86fc-50e5d5356f04,
  abstract     = {A. Pleijel has proved that in the case of the Laplacian on the square with Neumann condition, the equality in the Courant nodal theorem (Courant sharp situation) can only be true for a finite number of eigenvalues. We identify five Courant sharp eigenvalues for the Neumann Laplacian in the square, and prove that there are no other cases.},
  author       = {Helffer, Bernard and Persson Sundqvist, Mikael},
  issn         = {1609-3321},
  keyword      = {Nodal domains,Courant theorem,Square,Neumann},
  language     = {eng},
  number       = {3},
  pages        = {455--495},
  publisher    = {Independent University of Moscow},
  series       = {Moscow Mathematical Journal},
  title        = {Nodal domains in the square – the Neumann case},
  volume       = {15},
  year         = {2015},
}