A theorem on fine connectedness
type: Item
instance of: scholarly article
title: A theorem on fine connectedness
zbMATH Open document ID: 0952.31007
DOI: 10.1023/A:1008652304526
author: Visa Latvala
published in: Potential Analysis
publication date: 2000-12-28T00:00:00Z
review text: An open connected set in the \(p\)-fine topology, i.e. in the coarsest topology making all \(p\)-superharmonic functions continuous, is called a \(p\)-fine domain. The purpose of this note is to prove the following theorem. Let \(\Omega\subset{\mathbb R}^n\) be a \(p\)-fine domain for \(1<p\leq n\) and let \(E\subset{\mathbb R}^n\) be a \(p\)-polar. Then \(\Omega\setminus E\) is a \(p\)-fine domain. As an application of the main result, the author establishes a general version of minimum principle.
Mathematics Subject Classification ID: 31C15
Mathematics Subject Classification ID: 31C45
zbMATH DE Number: 1455889
zbMATH Keywords: fine topology
zbMATH Keywords: \(p\)-fine domain
zbMATH Keywords: polar sets
zbMATH Keywords: minimum principle
MaRDI profile type: Publication
full work available at URL: a:1008652304526
OpenAlex ID: W2348125748
description: scientific article; zbMATH DE number 1455889