Eigenvalues of the Laplacian on symmetric regions
type: Item
instance of: scholarly article
title: Eigenvalues of the Laplacian on symmetric regions
zbMATH Open document ID: 0824.35091
DOI: 10.1007/BF01194014
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 1995-11-12T00:00:00Z
review text: The author investigates the effect of domain symmetries on the multiplicity of the eigenvalues in the fixed membrane problem \[ \Delta u + \lambda u = 0 \text{ in } \Omega \subset \mathbb{R}^ n, \quad u = 0 \text{ on } \partial \Omega \] with \(C^ r\) boundary, \(r \geq 3\). He gives a very thorough discussion of how higher symmetry of \(\Omega\) implies higher multiplicity of eigenvalues.
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 736850
zbMATH Keywords: effect of domain symmetries on the multiplicity of the eigenvalues
author: Antônio L. Pereira
reviewed by: René Sperb
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 736850