On removable singularities of certain harmonic maps
type: Item
instance of: scholarly article
title: On removable singularities of certain harmonic maps
zbMATH Open document ID: 0605.58020
published in: Proceedings of the Japan Academy. Series A
publication date: 1985-01-01T00:00:00Z
review text: A weakly harmonic map \(u\in H^ 1(\Omega,M)\cap L^{\infty}(\Omega,M)\) of a domain \(\Omega \subset {\mathbb{R}}^ n\) into a Riemannian manifold \(M(\subset {\mathbb{R}}^ k)\) is said to be stationary if the energy of u precomposed with any 1-parameter family of diffeomorphisms (with compact support in \(\Omega)\) is stable up to first order. The main result here is a removable singularity theorem which states that, for \(\Omega =ball\), any stationary map u which is \(C^ 2\) in \(B\setminus\) center extends smoothly to B provided that \(\int_{B}| Du|^ n dx<\infty\).
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
zbMATH DE Number: 3977977
zbMATH Keywords: weakly harmonic map
zbMATH Keywords: removable singularity
author: Shōichirō Takakuwa
reviewed by: Gábor Tóth
MaRDI profile type: Publication
full work available at URL: pjaa.61.103
OpenAlex ID: W2043924267
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DOI: 10.3792/PJAA.61.103
description: scientific article; zbMATH DE number 3977977