Pleijel’s nodal domain theorem for free membranes

Polterovich, Iosif

doi:10.1090/S0002-9939-08-09596-8

Pleijel’s nodal domain theorem for free membranes
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Proc. Amer. Math. Soc. 137 (2009), 1021-1024 Request permission

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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