Pleijel's nodal domain theorem for free membranes

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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.
4 pages; to appear in the Proceedings of the AMS

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Spectral Theory, Analysis of PDEs, 35B05; 35P99

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http://salesiana.dossiersoluciones.com/handle/123456789/160752

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0805.1553
 http://arxiv.org/abs/0805.1553

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arXiv