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Colbois, Bruno
Nom
Colbois, Bruno
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Professeur ordinaire
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Bruno.Colbois@unine.ch
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- PublicationAccès libreSpectrum of the Laplacian with weights(2019-3-4)
; El Soufi, AhmadGiven 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.