Nodal domains in the square – the Neumann case
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8539801
- author
- Helffer, Bernard and Persson Sundqvist, Mikael LU
- organization
- publishing date
- 2015
- 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
- 2016-04-01 14:02:19
- date last changed
- 2022-03-14 03:22:17
@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}},
keywords = {{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}},
}