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Moscow Mathematical Journal, 2015, Volume 15, Number 3, Pages 455–495
DOI: https://doi.org/10.17323/1609-4514-2015-15-3-455-495 (Mi mmj571) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Nodal domains in the square – the Neumann case

Bernard Helfferab, Mikael Persson Sundqvistc

a Laboratoire Jean Leray, Université de Nantes, France
b Laboratoire de Mathématiques UMR CNRS 8628, Université Paris-Sud-Bât 425, F-91405 Orsay Cedex, France
c Lund University, Department of Mathematical Sciences, Lund, Sweden
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DOI: https://doi.org/10.17323/1609-4514-2015-15-3-455-495
Abstract: Å. 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.
Key words and phrases: nodal domains, Courant theorem, square, Neumann.
Received: November 28, 2014; in revised form March 4, 2015
Bibliographic databases:
Document Type: Article
MSC: 35B05, 35P20, 58J50
Language: English
Citation: Bernard Helffer, Mikael Persson Sundqvist, “Nodal domains in the square – the Neumann case”, Mosc. Math. J., 15:3 (2015), 455–495
Citation in format AMSBIB
\Bibitem{HelSun15}
\by Bernard~Helffer, Mikael~Persson~Sundqvist
\paper Nodal domains in the square~-- the Neumann case
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 3
\pages 455--495
\mathnet{http://mi.mathnet.ru/mmj571}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-3-455-495}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3427435}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000365392600004}
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