Pleijel’s nodal domain theorem for free membranes
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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.References
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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
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2457442