We consider the eigenvalues of the Laplacian, with a Neumann or Robin boundary condition, on an open, bounded, connected set in R-n with a C-2 boundary. We obtain upper bounds for the eigenvalues that have a corresponding eigenfunction that achieves equality in Courant's Nodal Domain theorem. In the case where the set is also assumed to be convex, we obtain explicit upper bounds in terms of some of the geometric quantities of the set.

Upper bounds for courant-sharp neumann and robin eigenvalues

Léna, Corentin
2020

Abstract

We consider the eigenvalues of the Laplacian, with a Neumann or Robin boundary condition, on an open, bounded, connected set in R-n with a C-2 boundary. We obtain upper bounds for the eigenvalues that have a corresponding eigenfunction that achieves equality in Courant's Nodal Domain theorem. In the case where the set is also assumed to be convex, we obtain explicit upper bounds in terms of some of the geometric quantities of the set.
File in questo prodotto:
File Dimensione Formato  
A10-Pleijel-upper-bounds.pdf

non disponibili

Tipologia: Published (publisher's version)
Licenza: Accesso privato - non pubblico
Dimensione 801.07 kB
Formato Adobe PDF
801.07 kB Adobe PDF Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3460391
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
social impact