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arXiv · 0805.1553

Pleijel's nodal domain theorem for free membranes

Iosif Polterovich
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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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Iosif Polterovich. 2008-05-11. Pleijel's nodal domain theorem for free membranes. https://arxiv.org/abs/0805.1553

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