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Pleijel's nodal domain theorem for free membranes
Author(s):
Iosif
Polterovich
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1021-1024.
MSC (2000):
Primary 35B05, 35P99
Posted:
September 25, 2008
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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
DOI:
10.1090/S0002-9939-08-09596-8
PII:
S 0002-9939(08)09596-8
Keywords:
Laplacian,
Neumann boundary conditions,
nodal domain
Received by editor(s):
March 24, 2008
Posted:
September 25, 2008
Additional Notes:
Research partially supported by NSERC and FQRNT
Communicated by:
Walter Craig
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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