Pleijel's nodal domain theorem for free membranes
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2008
- DOI:
- 10.48550/arXiv.0805.1553
- arXiv:
- arXiv:0805.1553
- Bibcode:
- 2008arXiv0805.1553P
- Keywords:
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- Mathematics - Spectral Theory;
- Mathematics - Analysis of PDEs;
- 35B05;
- 35P99
- E-Print:
- 4 pages