Spectrum of the Laplacian with weights View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-03

AUTHORS

Bruno Colbois, Ahmad El Soufi

ABSTRACT

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 L2 inner product weighted by ρ. Under some regularity conditions on ρ and σ, these eigenvalues are those of the operator -ρ-1div(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. More... »

PAGES

149-180

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10455-018-9621-5

DOI

http://dx.doi.org/10.1007/s10455-018-9621-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1105166407


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