Growth estimates for modified Green potentials in the upper-half space
type: Item
instance of: scholarly article
title: Growth estimates for modified Green potentials in the upper-half space
zbMATH Open document ID: 1220.31008
author: Lei Qiao
author: Guantie Deng
published in: Bulletin des Sciences Mathématiques
publication date: 2011-05-31T00:00:00Z
review text: The authors construct a modified Green potential in the upper-half space of the \(n\)-dimensional Euclidean space. The motivation is the modification of the Poisson kernel by subtracting some special harmonic polynomials which allowed Finkelstein and Scheinberg to solve the Dirichlet problem for the upper half-space with arbitrary continuous data. In the present article, the authors modify the Green function of order \(\alpha\) for the upper half-space by subtracting some combinations of suitable ultraspherical (Gegenbauer) polynomials from the kernel. The behavior at infinity of this modified Green function is also given. The finding is that outside a Borel set with controlled capacity, the Green function grows slower than an appropriate power of the absolute value of the argument times an appropriate power of the last (positive) coordinate of the argument. A geometric approach using certain covering with balls of the aforementioned Borel set is also provided.
reviewed by: Żywomir Dinew
Mathematics Subject Classification ID: 31B10
Mathematics Subject Classification ID: 31C05
zbMATH DE Number: 5902654
zbMATH Keywords: modified Green potential
zbMATH Keywords: capacity
MaRDI profile type: Publication
full work available at URL: j.bulsci.2010.08.002
OpenAlex ID: W2088776481
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DOI: 10.1016/J.BULSCI.2010.08.002
description: scientific article; zbMATH DE number 5902654