The highest smoothness of the Green function implies the highest density of a set
type: Item
instance of: scholarly article
title: The highest smoothness of the Green function implies the highest density of a set
zbMATH Open document ID: 1061.31003
DOI: 10.1007/BF02385477
published in: Arkiv för Matematik
publication date: 2004-09-28T00:00:00Z
review text: Let \(E\) be a subset of the interval \([0,1]\) and \(\Omega\) be the complement of \(E\) in the extended plane. The author observes that the density of \(E\) at zero is somehow related to the smoothness of the Green function \(g_\Omega\) of \(\Omega\) at the origin. Among other results, he shows that if the Green function \(g_\Omega\) satisfies a Lipschitz condition \(g_\Omega(z)\leq c|z|^{1/2}\), \(z\in C\) at the origin, then the density of \(E\) in a small neighborhood of zero, measured in terms of logarithmic capacity, is arbitrarily close to the density of \([0,1]\) in that neighborhood.
Mathematics Subject Classification ID: 31A15
Mathematics Subject Classification ID: 35A08
zbMATH DE Number: 2103846
zbMATH Keywords: Green function
zbMATH Keywords: logarithmic capacity
zbMATH Keywords: Hölder's condition
author: V. V. Andrievskii
reviewed by: Yusuf Avci
MaRDI profile type: Publication
cites work: On the Green function for a complement of a finite number of real intervals
cites work: Q4328333
cites work: Q4360405
description: scientific article; zbMATH DE number 2103846