The Martin kernel for unbounded domains
type: Item
instance of: scholarly article
title: The Martin kernel for unbounded domains
zbMATH Open document ID: 1188.31006
published in: Potential Analysis
publication date: 2010-04-15T00:00:00Z
review text: Let \((x_{1},\widetilde{x})\) denote a typical point of \(\mathbb{R}\times \mathbb{R}^{d-1}\), where \(d\geq 3\), and let \(a:[0,\infty )\rightarrow (0,\infty )\) be Lipschitz. This paper is concerned with unbounded domains \(D\) of the form \(\{(x_{1},\widetilde{x}):x_{1}>0,\;\left| \widetilde{x}\right| <a(x_{1})\}\). Under certain hypotheses on \(a(\cdot )\) the author establishes: (i)~that the Martin boundary of \(D\) is homeomorphic to \(\partial D\cup \{\infty \}\) and all boundary points are minimal; (ii)~the asymptotic behaviour of the Martin kernel with pole at \(\infty \) in terms of the function \(a(\cdot )\).
reviewed by: Stephen J. Gardiner
Mathematics Subject Classification ID: 31C35
Mathematics Subject Classification ID: 31B05
zbMATH DE Number: 5693237
zbMATH Keywords: harmonic functions
zbMATH Keywords: Martin boundary
zbMATH Keywords: asymptotic behaviour
author: Dante de Blassie
MaRDI profile type: Publication
full work available at URL: s11118-009-9156-2
OpenAlex ID: W2140213815
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DOI: 10.1007/S11118-009-9156-2
description: scientific article; zbMATH DE number 5693237