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Eigenvalues of elliptic operators with density
Auteur(s)
Provenzano, Luigi
Date de parution
2018-5-17
In
Calc. Var. Partial Differential Equations
No
57
De la page
1
A la page
35
Résumé
We consider eigenvalue problems for elliptic operators of arbitrary order $2m$ subject to Neumann boundary conditions on bounded domains of the Euclidean $N$-dimensional space. We study the dependence of the eigenvalues upon variations of mass density. In particular we discuss the existence and characterization of upper and lower bounds under both the condition that the total mass is fixed and the condition that the $L^{\frac{N}{2m}}$-norm of the density is fixed. We highlight that the interplay between the order of the operator and the space dimension plays a crucial role in the existence of eigenvalue bounds.
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Type de publication
journal article
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