A Wiener-type condition for Hölder continuity for Green's functions
type: Item
instance of: scholarly article
title: A Wiener-type condition for Hölder continuity for Green's functions
zbMATH Open document ID: 1135.31004
published in: Acta Mathematica Hungarica
publication date: 2007-01-08T00:00:00Z
review text: The author studies local properties of the Green function of the complement of a compact set \(E\) in \(\mathbb R^d\), \(d>2\). A Wiener type characterization for the Hölder continuity of the Green function is given. The obtained density condition is necessary, and it is sufficient as well, provided \(E\) satisfies the cone condition. It is also shown that the Hölder condition for the Green function at a boundary point can be equivalently stated in terms of the equilibrium measure and the solution to the corresponding Dirichlet problem.
Mathematics Subject Classification ID: 31B25
Mathematics Subject Classification ID: 31B35
zbMATH DE Number: 5082262
zbMATH Keywords: Green's function
zbMATH Keywords: Hölder continuity
zbMATH Keywords: Wiener's theorem
zbMATH Keywords: cone condition
zbMATH Keywords: Newtonian capacity
author: F. Toókos
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: s10474-006-0039-3
OpenAlex ID: W1979397357
DOI: 10.1007/S10474-006-0039-3
description: scientific article; zbMATH DE number 5082262