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- W1634577630 abstract "AA. Pleijel (1956) has proved that in the case of the Laplacian with Dirichlet condition, the equality in the Courant nodal theorem (Courant sharp situation) can only be true for a finite number of eigenvalues when the dimension is $geq 2$. This is only recently that Polterovich solved the problem for the Neumann problem. A question coming from the theory of spectral minimal partitions has motivated the analysis of the cases when one has equality in Courant's theorem. In this note, we identify three Courant sharp eigenvalues for the Neumann Laplacian in the disc, and prove that there are no other cases." @default.
- W1634577630 created "2016-06-24" @default.
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- W1634577630 date "2015-06-12" @default.
- W1634577630 modified "2023-09-27" @default.
- W1634577630 title "Nodal domains in the disc---the Neumann case" @default.
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