Sharp estimates for the Green function in Lipschitz domains
type: Item
instance of: scholarly article
title: Sharp estimates for the Green function in Lipschitz domains
zbMATH Open document ID: 0971.31005
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-10-24T00:00:00Z
review text: The main result of this paper is a precise estimate for the Green function of a bounded Lipschitz domain in \(\mathbb{R}^{d}\) for \(d\geq 3\). The author provides a careful analysis of the dependence of the constants appearing in the estimates. Applications are given to provide short proofs of precise estimates for the Martin kernel of Lipschitz domains, for the Green function of \(C^{1,1}\) domains, and a short proof of the 3G theorem. Moreover, the author shows how these results are connected to the boundary Harnack principle.
Mathematics Subject Classification ID: 31B20
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1439366
zbMATH Keywords: Green function
zbMATH Keywords: Martin kernel
zbMATH Keywords: Lipschitz domains
zbMATH Keywords: boundary Harnack principle
zbMATH Keywords: 3G theorem
zbMATH Keywords: \(C^{1,1}\) domains
Wikidata QID: Q110598177
author: Krzysztof Bogdan
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6673
OpenAlex ID: W2000167964
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DOI: 10.1006/JMAA.1999.6673
description: scientific article; zbMATH DE number 1439366