An extremal problem on the minimum of energy for space condensers
type: Item
instance of: scholarly article
title: An extremal problem on the minimum of energy for space condensers
zbMATH Open document ID: 0665.31003
DOI: 10.1007/BF01057292
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Let \(E^+\), \(E^-\) be closed sets in \({\mathbb{R}}^ p\), \(p\geq 3\) and one of them bounded. The author considers the problem of the minimisation of the energy \[ \iint_{{\mathbb{R}}^ p\times {\mathbb{R}}^ p}| x- y|^{2-p} d\nu (x) d\nu (y), \] where the charge \(\nu\) has a representation \(\nu =\nu^+-\nu^-.\) The charges \(\nu^{\pm}\) satisfy the following conditions: \(\sup p \nu^{\pm}\subset E^{\pm},\quad \nu^{\pm}(1)=1.\) Necessary and sufficient conditions for the existence of the extremal charge are stated.
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 78A25
zbMATH DE Number: 4088006
zbMATH Keywords: Newtonian energy
zbMATH Keywords: Green capacity
zbMATH Keywords: condensator
zbMATH Keywords: minimisation of the energy
zbMATH Keywords: charge
author: N. Zorii
MaRDI profile type: Publication
cites work: Q5547883
cites work: Q5840458
cites work: Les potentiels d'energie finie
description: scientific article; zbMATH DE number 4088006