Partial regularity for stationary harmonic maps into spheres
type: Item
instance of: scholarly article
title: Partial regularity for stationary harmonic maps into spheres
zbMATH Open document ID: 0754.58007
DOI: 10.1007/BF00375587
author: S. Singh
published in: Archive for Rational Mechanics and Analysis
publication date: 1992-09-27T00:00:00Z
review text: Let \(\Omega\subset \mathbb{R}^ n\) denote an open set and consider a weak solution \(u\in H^{1,2}(\Omega,S^{m-1})\) of \(-\Delta u=u\cdot |\nabla u|^ 2\), i.e. a weak solution of the Euler-Lagrange equation of the energy functional \(\int_ \Omega|\nabla u|^ 2dx\) among all mappings from \(\Omega\) into the sphere \(S^{m-1}\). If in addition the monotonicity inequality holds for \(u\) then \(u\in C^ \infty(\Omega-\Sigma,\mathbb{R}^ m)\) for some relatively closed subset \(\Sigma\) of \(\Omega\) s.t. \(H^{n-2}(\Sigma)=0\).
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 58002
zbMATH Keywords: stationary harmonic maps
zbMATH Keywords: partial regularity
zbMATH Keywords: weak solution
zbMATH Keywords: Euler- Lagrange equation
zbMATH Keywords: sphere
reviewed by: M. Fuchs
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00375587
OpenAlex ID: W1971218181
description: scientific article; zbMATH DE number 58002