The principal eigenvalue and maximum principle for second order elliptic operators on Riemannian manifolds
type: Item
instance of: scholarly article
title: The principal eigenvalue and maximum principle for second order elliptic operators on Riemannian manifolds
zbMATH Open document ID: 0892.58082
author: Pablo Padilla
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-07-15T00:00:00Z
review text: \textit{H. Berestycki}, \textit{L. Nirenberg} and \textit{S. R. S. Varadhan} [Commun. Pure Appl. Math. 47, No. 1, 47-92 (1994; Zbl 0806.35129)] and \textit{H. Berestycki} and \textit{L. Nirenberg} [Bol. Soc. Bras. Mat., Nova Sér. 22, No. 1, 1-37 (1991; Zbl 0784.35025)] wrote on the maximum principle and principal eigenvalues of second order operators on general domains. The author extends this work to Riemannian manifolds. He shows that the refined maximum principle holds for a second order elliptic operator on a manifold if and only if the principal eigenvalue is positive. The work is motivated by the study of symmetry properties of positive solutions of elliptic equations on symmetric domains.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35P15
zbMATH DE Number: 1005656
zbMATH Keywords: maximum principle
zbMATH Keywords: principal eigenvalue
zbMATH Keywords: elliptic operator
reviewed by: Peter B. Gilkey
MaRDI profile type: Publication
OpenAlex ID: W2023846856
Wikidata QID: Q115395408
cites work: On the method of moving planes and the sliding method
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cites work: Q5548618
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DOI: 10.1006/JMAA.1997.5139
description: scientific article; zbMATH DE number 1005656