Eigenvalues of elliptic operators with density

2017/06/01 by Colbois, Bruno, Provenzano, Luigi · 1 citation
#35J40 #35P15 #35P20 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1706.00243

Abstract

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 and 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^(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.

Cited by

• Optimal eigenvalues on a metric graph with densities

Related

• Estimates for eigenvalues of the operator L_r
• Eigenvalues of the Neumann Laplacian with density and sharp Sobolev-Orlicz embeddings
• Estimates for eigenvalues of a system of of elliptic equations and of the biharmonic operator
• Domain dependence of eigenvalues of elliptic type operators
• Eigenvalues of the Laplacian with density