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Spectrum of the Laplacian with weights
Auteur(s)
El Soufi, Ahmad
Date de parution
2019-3-4
In
Annals of Global Analysis and Geometry
Vol.
2
No
55
De la page
149
A la page
180
Revu par les pairs
1
Résumé
Given a compact Riemannian manifold $(M,g)$ and two positive functions $\rho$ and $\sigma$, we are interested in the eigenvalues of the Dirichlet energy functional weighted by $\sigma$, with respect to the $L^2$ inner product weighted by $\rho$. Under some regularity conditions on $\rho$ and $\sigma$, these eigenvalues are those of the operator
$-\rho^{-1} \mbox{div}(\sigma \nabla u)$
with Neumann conditions on the boundary if $\partial M\ne \emptyset$.
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.
$-\rho^{-1} \mbox{div}(\sigma \nabla u)$
with Neumann conditions on the boundary if $\partial M\ne \emptyset$.
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.
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journal article
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