Boundary Harnack principle for separated semihyperbolic repellers, harmonic measure applications
type: Item
instance of: scholarly article
title: Boundary Harnack principle for separated semihyperbolic repellers, harmonic measure applications
zbMATH Open document ID: 0857.31006
DOI: 10.4171/RMI/200
author: Zoltán M. Balogh
author: Alexander Volberg
published in: Revista Matemática Iberoamericana
publication date: 1996-10-10T00:00:00Z
full work available at URL: https://eudml.org/doc/39506
review text: An extensive literature on the boundary Harnack principle focusses on the following result: Let \(\Omega\) be a domain in \(\mathbb{R}^n\) with certain geometric property of \(\partial \Omega\) and let \(u,v\) be positive harmonic functions on \(\Omega\) vanishing on \(V\cap \partial\Omega\) \((V\) is an open set). Then there exists a constant \(C=C(\Omega,V,K)\) such that \[ {u(x)/v(x) \over u(y)/v(y)} \leq C, \quad \text{for } x,y\in K\cap \Omega, \] where \(K\) is a compact in \(V\). The authors extend investigations of the previous result to a wider class, namely to the class of John domains.
Mathematics Subject Classification ID: 31C05
zbMATH DE Number: 933287
zbMATH Keywords: boundary Harnack principle
zbMATH Keywords: harmonic functions
zbMATH Keywords: John domains
reviewed by: Sophia L. Kalpazidou
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 933287