Illinois Journal of Mathematics

On the second eigenvalue of the Laplacian in an annulus

Liangpan Li

Full-text: Open access

Abstract

It is shown that the second eigenvalue of the Laplacian with either Dirichlet or Neumann boundary conditions in an annulus in a Euclidean space, or in a sphere, or in a hyperbolic space of dimension $n>1$ has multiplicity $n$.

Article information

Source
Illinois J. Math., Volume 51, Number 3 (2007), 913-925.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258131110

Digital Object Identifier
doi:10.1215/ijm/1258131110

Mathematical Reviews number (MathSciNet)
MR2379730

Zentralblatt MATH identifier
1155.35017

Subjects
Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]
Secondary: 35P05: General topics in linear spectral theory

Citation

Li, Liangpan. On the second eigenvalue of the Laplacian in an annulus. Illinois J. Math. 51 (2007), no. 3, 913--925. doi:10.1215/ijm/1258131110. https://projecteuclid.org/euclid.ijm/1258131110


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