Correction to ``Unbounded quadrature domains in \({\mathbb{R}}^ n\) \((n{\geq{}}3)\)''
type: Item
instance of: scholarly article
title: Correction to ``Unbounded quadrature domains in \({\mathbb{R}}^ n\) \((n{\geq{}}3)\)''
zbMATH Open document ID: 0767.31006
DOI: 10.1007/BF03041074
author: Henrik Shahgholian
published in: Journal d'Analyse Mathématique
publication date: 1993-06-29T00:00:00Z
review text: The statement in Lemma 1.5 in the author's paper [J. Anal. Math. 56, 281- 291 (1991; Zbl 0745.31003)] is not true. In fact, the function \(g(t)=t^ n\log^{-2}(t)\) is a counterexample to Lemma 1.5. The incorrect proof given there depends on the wrong assertion that \(\int^ \infty_{r'}(t\log^ nt)^{-1}dt\) is divergent for \(n\geq 2\). To save Theorem 1.4 we have to change the statement of Lemma 1.1. Namely, part (b) of Lemma 1.1 should read \[ |\nabla u(y)|\leq C\bigl[1+| y-\xi|\log\bigl({|\xi|\over| y- \xi|}\bigr)\bigr], \] where \(\xi\) is any point on \(\partial\Omega\).
Mathematics Subject Classification ID: 31B20
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 221313
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf03041074
OpenAlex ID: W71946525
Recommended article: Unbounded quadrature domains in \({\mathbb{R}{}}^ n\quad (n \geq{} 3)\)
Recommended article: Correction to: ``Nearly quartic mappings in \(\beta\)-homogeneous \(F\)-spaces''
Recommended article: Correction to: ``On the approximation of unbounded convex sets by polyhedra''
Recommended article: Q2960794
Recommended article: Correction to: ``Boundary unique continuation on \(C^1\)-Dini domains and the size of the singular set''
Recommended article: Correction to: ``Polynomials with bounds and numerical approximation''
Recommended article: Corrigendum to: ``The \(n\)-width of the unit ball of \(H^ q\)''
Recommended article: Correction to: ``Infinite dimensional holomorphic homogeneous regular domains''
description: scientific article; zbMATH DE number 221313