An overdetermined problem for harmonic functions
type: Item
instance of: scholarly article
title: An overdetermined problem for harmonic functions
zbMATH Open document ID: 1227.31004
author: Robert Dalmasso
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-10-24T00:00:00Z
review text: The author shows that any open bounded connected subset of \(\mathbb{R}^n\) which has real-analytic boundary and which carries \(n\) harmonic functions satisfying an appropriate partial differential equation involving the curvature at the boundary is homeomorphic to a ball. The proof uses a result by \textit{J. Serrin} [Arch. Ration. Mech. Anal. 43, 304--318 (1971; Zbl 0222.31007)] and it is based on a long equation manipulation.
reviewed by: Athanase Papadopoulos
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 31B35
Mathematics Subject Classification ID: 31B20
zbMATH DE Number: 5962673
zbMATH Keywords: harmonic function
zbMATH Keywords: overdetermined problem
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.07.030
OpenAlex ID: W2025699070
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DOI: 10.1016/J.JMAA.2011.07.030
description: scientific article; zbMATH DE number 5962673