Weak monotonicity inequality and partial regularity for harmonic maps
type: Item
instance of: scholarly article
title: Weak monotonicity inequality and partial regularity for harmonic maps
zbMATH Open document ID: 0948.58014
DOI: 10.1007/BF02874254
author: Shusen Yan
author: Yaotian Shen
published in: Science in China. Series A
publication date: 2000-02-17T00:00:00Z
review text: The paper is concerned with weakly harmonic maps from a domain in \(\mathbb{R}^3\) to \(S^2\). It is shown that for such maps a local weak form of the monotonicity inequality is equivalent to certain bounds for the energy on balls centered in singular points. This is used to prove the existence of non-minimizing solutions to the Dirichlet problem having at most isolated singularities. By analyzing axially symmetric maps, it is also shown that the local form of the weak monotonicity inequality is not equivalent to the global one. Furthermore, examples with non-isolated singularities are constructed.
reviewed by: Andreas Gastel
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 1342683
zbMATH Keywords: harmonic maps
zbMATH Keywords: weak monotonicity inequality
zbMATH Keywords: \(\varepsilon\)-regularity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1342683