Greenian potentials and concavity
type: Item
instance of: scholarly article
title: Greenian potentials and concavity
zbMATH Open document ID: 0584.31003
DOI: 10.1007/BF01455935
author: Christer Borell
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164004
review text: Let D be a bounded domain in \({\mathbb{R}}^ n\), \(v\geq 0\) be a continuous function in D and \(G_ v\) be the Green operator relative to \(- (1/2)\Delta +v\). The author proves that the corresponding Green potentials satisfy a Brunn-Minkowski type inequality and obtains the following result: If D is bounded convex and if \(f: D\to]0,\infty [\) and \(v^{-1/2}\) are concave (v\(\equiv 0\) or \(v>0)\), then \((G_ v f^ p)^{1/(2+p)}\) is concave, \(0\leq p\leq 1\).
Mathematics Subject Classification ID: 31B15
Mathematics Subject Classification ID: 31A10
Mathematics Subject Classification ID: 31B99
zbMATH DE Number: 3935425
zbMATH Keywords: Green operator
zbMATH Keywords: Green potentials
zbMATH Keywords: Brunn-Minkowski type inequality
reviewed by: Victor Anandam
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3935425