Aspects of potential theory on manifolds, linear and non-linear
type: Item
instance of: scholarly article
title: Aspects of potential theory on manifolds, linear and non-linear
zbMATH Open document ID: 1205.31005
author: S. Pigola
author: M. Rigoli
author: Alberto G. Setti
published in: Milan Journal of Mathematics
publication date: 2009-11-02T00:00:00Z
review text: The authors describe some aspects of potential theory on Riemannian manifolds, concentrating on Liuoville-type theorems and their relationships with parabolicity and stochastic completeness of the underlying manifold. The paper starts with an overview of parabolicity, then goes into the relationship between stochastic completeness and the weak maximum principle, and then some possible generalizations of these concepts to the case of nonlinear operators such as the \(\phi\)-Laplacian with \(\phi\) satisfying certain conditions. Particular attention is paid to the \(p\)-Laplacian, \(p>1\), which is a special case of the \(\phi\)-Laplacian with \(\phi(t)=t^{p-1}\).
reviewed by: Renming Song
Mathematics Subject Classification ID: 31C12
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 58J05
zbMATH DE Number: 5624126
zbMATH Keywords: potential theory on manifolds
zbMATH Keywords: Liouville-type theorems
zbMATH Keywords: parabolicity
zbMATH Keywords: stochastic completeness
zbMATH Keywords: \(p\)-Laplacian
MaRDI profile type: Publication
full work available at URL: s00032-008-0084-1
OpenAlex ID: W2172123234
DOI: 10.1007/S00032-008-0084-1
description: scientific article; zbMATH DE number 5624126