Pleijel's nodal domain theorem for free membranes

Details Pleijel's nodal domain theorem for free membranes Pleijel's nodal domain theorem for free membranes

2008-05-11

arxiv.org/abs/0805.1553v1

Mathematics

Spectral Theory

4 pages; to appear in the Proceedings of the AMS

Scientific paper

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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