\(N\)-capacity, \(N\)-harmonic radius and \(N\)-harmonic transplantation
type: Item
instance of: scholarly article
title: \(N\)-capacity, \(N\)-harmonic radius and \(N\)-harmonic transplantation
zbMATH Open document ID: 1107.31005
author: Wei Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-01-09T00:00:00Z
review text: The method of harmonic transplantation was introduced by \textit{J. Hersch} [Comment. Math. Helv. 44, 354--366 (1969; Zbl 0175.12002)]. This method gives upper bounds for domain functionals whereas symmetrization gives lower bounds. The author generalizes this method to the case of \(n\)-harmonic functions defined on regular domains. The \(n\)-Robin function and the \(n\)-harmonic radius are introduced and their basic properties given. A new proof for the isoperimetric inequality for the \(n\)-capacity is given and the isoperimetric inequality for the \(n\)-harmonic radius is proved.
reviewed by: M. Vuorinen
Mathematics Subject Classification ID: 31C15
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 28A75
zbMATH DE Number: 5083266
zbMATH Keywords: harmonic transplantation
zbMATH Keywords: isoperimetric inequality
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.04.017
OpenAlex ID: W1992932372
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DOI: 10.1016/J.JMAA.2006.04.017
description: scientific article; zbMATH DE number 5083266