The discrete spectrum of the Laplace operator in a cylinder with locally perturbed boundary
type: Item
instance of: scholarly article
title: The discrete spectrum of the Laplace operator in a cylinder with locally perturbed boundary
zbMATH Open document ID: 1087.35074
author: A. L. Delitsyn
published in: Differential Equations
publication date: 2005-06-17T00:00:00Z
review text: The author considers a cylindrical domain \(Q_{1}\) in \(\mathbb R^{3}\) obtained by deforming a right cylinder of the form \(\Omega\times\mathbb R\) in a part \(\Omega\times [z_{1},z_{2}]\). Here \(\Omega\) is an open connected subset of \(\mathbb R^{2}\), and \(z_{1},z_{2}\in \mathbb R\). The author proves that under suitable regularity conditions on \(Q_{1}\), the Laplace operator with Dirichlet boundary conditions in \(Q_{1}\) has at least one eigenvalue to which corresponds one eigenfunction in the class \(L^{2}(Q_{1})\cap C^{\infty} (\overline{Q_{1}})\).
reviewed by: Massimo Lanza de Cristoforis
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 2176637
zbMATH Keywords: Dirichlet Laplacian
zbMATH Keywords: unbounded domains
MaRDI profile type: Publication
full work available at URL: b:dieq.0000033710.40234.3c
OpenAlex ID: W2006212977
DOI: 10.1023/B:DIEQ.0000033710.40234.3C
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description: scientific article; zbMATH DE number 2176637