Pleijel's nodal domain theorem for free membranes
Spectral Theory
2008-05-13 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.0805.1553,
title = {Pleijel's nodal domain theorem for free membranes},
author = {Iosif Polterovich},
journal= {arXiv preprint arXiv:0805.1553},
year = {2008}
}
Comments
4 pages; to appear in the Proceedings of the AMS