In [2], the number of nodal domains for the eigenfunctions of the Neumann or Robin Laplacian is bounded from above using the classical (Euclidean) Faber-Krahn inequality. However, in an arbitrary Riemannian manifold, this inequality might not hold. We supply the missing arguments in two dimensions and outline a modification of the method, which preserves most of the results, in n dimensions.
Corrections "Upper bounds for Courant-sharp Neumann and Robin eigenvalues"
LENA, Corentin
;
2026
Abstract
In [2], the number of nodal domains for the eigenfunctions of the Neumann or Robin Laplacian is bounded from above using the classical (Euclidean) Faber-Krahn inequality. However, in an arbitrary Riemannian manifold, this inequality might not hold. We supply the missing arguments in two dimensions and outline a modification of the method, which preserves most of the results, in n dimensions.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
corrigendum-BSMF-GittinsLena-revised.pdf
accesso aperto
Tipologia:
Accepted (AAM - Author's Accepted Manuscript)
Licenza:
Accesso gratuito
Dimensione
212.83 kB
Formato
Adobe PDF
|
212.83 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
