We show that equality in Courant's nodal domain theorem can only be reached for a finite number of eigenvalues of the Neumann Laplacian, in an open, bounded, and connected subset of R-n with a C-1,C-1 boundary, when n >= 2. This result is analogous to the theorem proved by Pleijel in 1956 for the Dirichlet Laplacian. We also show that the argument and the result extend to a class of Robin boundary conditions.

PLEIJEL'S NODAL DOMAIN THEOREM FOR NEUMANN AND ROBIN EIGENFUNCTIONS

Léna, Corentin
2019

Abstract

We show that equality in Courant's nodal domain theorem can only be reached for a finite number of eigenvalues of the Neumann Laplacian, in an open, bounded, and connected subset of R-n with a C-1,C-1 boundary, when n >= 2. This result is analogous to the theorem proved by Pleijel in 1956 for the Dirichlet Laplacian. We also show that the argument and the result extend to a class of Robin boundary conditions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3460392
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