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Pleijel's nodal domain theorem for free membranes


Author: Iosif Polterovich
Journal: Proc. Amer. Math. Soc. 137 (2009), 1021-1024
MSC (2000): Primary 35B05, 35P99
DOI: https://doi.org/10.1090/S0002-9939-08-09596-8
Published electronically: September 25, 2008
MathSciNet review: 2457442
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Abstract: We prove an analogue of Pleijel's nodal domain theorem for piecewise analytic planar domains with Neumann boundary conditions. This confirms a conjecture made by Pleijel in 1956. The proof is a combination of Pleijel's original approach and an estimate due to Toth and Zelditch for the number of boundary zeros of Neumann eigenfunctions.


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Additional Information

Iosif Polterovich
Affiliation: Département de Mathématiques et de Statistique, Université de Montréal, CP 6128 succ. Centre-Ville, Montréal, Quebec H3C 3J7, Canada
Email: iossif@dms.umontreal.ca

DOI: https://doi.org/10.1090/S0002-9939-08-09596-8
Keywords: Laplacian, Neumann boundary conditions, nodal domain
Received by editor(s): March 24, 2008
Published electronically: September 25, 2008
Additional Notes: Research partially supported by NSERC and FQRNT
Communicated by: Walter Craig
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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