Inequalities between Dirichlet and Neumann eigenvalues
type: Item
instance of: scholarly article
title: Inequalities between Dirichlet and Neumann eigenvalues
zbMATH Open document ID: 0608.35047
DOI: 10.1007/BF00279862
author: Hans F. Weinberger
author: Howard A. Levine
published in: Archive for Rational Mechanics and Analysis
publication date: 1986-01-01T00:00:00Z
review text: Consider a smooth enough bounded open set D in \({\mathbb{R}}^ n\) and \(\{\lambda_ k\}\) (resp. \(\{\mu_ k\})\) the eigenvalues of: \(\Delta u+\lambda u=0\) for Dirichlet (resp. Neumann) problem. The authors prove inequalities of the form: \(\mu_{k+R}<\lambda_ k\) for \(k\geq 1.\) In particular if D is convex they obtain: \(\mu_{k+n}<\lambda_ k\) for \(k\geq 1\).
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 3983738
zbMATH Keywords: Dirichlet
zbMATH Keywords: Neumann
zbMATH Keywords: inequalities
zbMATH Keywords: convex
reviewed by: Didier Robert
MaRDI profile type: Publication
cites work: Symmetry Theorems Related to Pompeiu's Problem
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description: scientific article; zbMATH DE number 3983738