Commentarii Mathematici Helvetici

, Volume 70, Issue 1, pp 310–338 | Cite as

Uniqueness for the harmonic map flow from surfaces to general targets

  • Alexandre Freire
Article

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 inH1(Mx[0,T]; N) whose energy is non-increasing in time and having the same initial datau0∈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 of(0,T)c.

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Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Alexandre Freire
    • 1
  1. 1.Department of MathematicsUniversity of TennesseeKnoxvilleUSA

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