Restricted mean value property on \(\mathbb{R}^ d, d\leq 2\)
type: Item
instance of: scholarly article
title: Restricted mean value property on \(\mathbb{R}^ d, d\leq 2\)
zbMATH Open document ID: 0847.31001
author: Wolfhard Hansen
author: Nikolai Nadirashvili
published in: Expositiones Mathematicae
publication date: 1996-10-15T00:00:00Z
review text: Let \(r\) be a strictly positive real function on \(\mathbb{R}\) such that \(r(x) \leq |x |+ c\) where \(c\) is some positive constant. A nonnegative lower-semi-continuous function \(f\) is said to be \(r\) supermedian if the integral of \(f\) on the intervals of center \(x\) and radius \(r(x)\) is not greater than \(f(x)\) for any \(x\). It is proved in this (3 page) paper that such a function is necessarily constant using Bauer's minimum principle.
Mathematics Subject Classification ID: 31A05
zbMATH DE Number: 783958
zbMATH Keywords: mean value
zbMATH Keywords: Veech's conjecture
zbMATH Keywords: harmonic functions
zbMATH Keywords: supermedian function
zbMATH Keywords: Bauer's minimum principle
reviewed by: Jean Lacroix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 783958