Pleijel’s nodal domain theorem for Neumann and Robin eigenfunctions
Corentin Léna · Annales de l’institut Fourier · 2019
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 , 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.