Pleijel’s Nodal Domain Theorem for Free Membranes
نویسنده
چکیده
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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تاریخ انتشار 2008