Uniqueness for the harmonic map flow in two dimensions
type: Item
instance of: scholarly article
title: Uniqueness for the harmonic map flow in two dimensions
zbMATH Open document ID: 0814.35057
DOI: 10.1007/BF01190893
author: Alexandre Freire
published in: Calculus of Variations and Partial Differential Equations
publication date: 1995-02-06T00:00:00Z
review text: The following uniqueness theorem is proved: Let \(M\) be a 2-dimensional Riemannian manifold with smooth boundary. If \(u,v \in H^ 1 (M \times [0,T]\); \(S^ N)\) are weak heat flows for harmonic maps, with nonincreasing energy in time, and with the same initial data and boundary value, then \(u=v\). This theorem differs from a similar result due to T. Rivière, in which a small energy assumption was made but without the nonincreasing energy assumption.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 58J35
zbMATH DE Number: 719389
zbMATH Keywords: Hodge decomposition
zbMATH Keywords: uniqueness theorem
zbMATH Keywords: weak heat flows for harmonic maps
reviewed by: Kung Ching Chang
MaRDI profile type: Publication
cites work: On the evolution of harmonic mappings of Riemannian surfaces
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description: scientific article; zbMATH DE number 719389