SPECTRUM OF THE LAPLACIAN WITH WEIGHTS - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

SPECTRUM OF THE LAPLACIAN WITH WEIGHTS

Résumé

Given a compact Riemannian manifold (M, g) and two positive functions ρ and σ, we are interested in the eigenvalues of the Dirichlet energy functional weighted by σ, with respect to the L 2 inner product weighted by ρ. Under some regularity conditions on ρ and σ, these eigenvalues are those of the operator ρ^{-1} div(σ∇u) with Neumann conditions on the boundary if ∂M = ∅. We investigate the effect of the weights on eigenvalues and discuss the existence of lower and upper bounds under the condition that the total mass is preserved.
Fichier principal
Vignette du fichier
Eigenvalue-density-submitted.pdf (335.33 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01330456 , version 1 (10-06-2016)

Identifiants

Citer

Bruno Colbois, Ahmad El Soufi. SPECTRUM OF THE LAPLACIAN WITH WEIGHTS. 2016. ⟨hal-01330456⟩
144 Consultations
253 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More