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Uniqueness for the harmonic map flow from surfaces to general targets

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Commentarii Mathematici Helvetici

An Erratum to this article was published on 01 December 1996

Abstract

LetM be a two-dimensional compact Riemannian manifold with smooth (possibly empty) boundary,N an arbitrary compact manifold. Ifu andv are weak solutions of the harmonic map flow inH 1(Mx[0,T]; N) whose energy is non-increasing in time and having the same initial datau 0∈H1(M, N) (and same boundary values if ∂M≠Ø) thenu=v. Combined with a result of M. Struwe, this shows any suchu is smooth in the complement of a finite subset ofM×(0,T)c.

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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee, 37996-1300, Knoxville, TN, USA

    Alexandre Freire

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  1. Alexandre Freire
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Mathematics subject classification (1991): 35K55, 58E20, 58G11.

An erratum to this article is available at http://dx.doi.org/10.1007/BF02566422.

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Freire, A. Uniqueness for the harmonic map flow from surfaces to general targets. Commentarii Mathematici Helvetici 70, 310–338 (1995). https://doi.org/10.1007/BF02566010

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  • DOI: https://doi.org/10.1007/BF02566010

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