First eigenvalue for the \(p\)-Laplace operator
type: Item
instance of: scholarly article
title: First eigenvalue for the \(p\)-Laplace operator
zbMATH Open document ID: 0948.35090
DOI: 10.1016/S0362-546X(98)00266-1
author: Ana-Maria Matei
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-11-19T00:00:00Z
review text: This paper deals with the first eigenvalue of the \(p\)-Laplacian operator \(\Delta_p\), \(p\geq 1\), on \(m\)-dimensional Riemannian manifolds. The first result is a generalization of a comparison theorem proved by \textit{S. Y. Cheng} [Math. Z. 143, 289-297 (1975; Zbl 0329.53035)] for \(p=2\). The next result is a Faber-Krahn-type isoperimetric inequality for the \(p\)-Laplacian in bounded domains of a manifold with positive Ricci curvature, which was obtained in the case of the Laplacian by \textit{P. Bérard}, \textit{D. Meyer} [Ann. Sci. Éc. Norm. Supér., IV. Sér. 15, 513-541 (1982; Zbl 0527.35020)]. A comparison result of Lichnerowicz-Obata and Cheeger-type estimates are also generalized to the case \(p>1\).
reviewed by: Bodo Dittmar
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1419636
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: eigenvalue isoperimetric inequality
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00266-1
OpenAlex ID: W2053860749
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description: scientific article; zbMATH DE number 1419636