Uniqueness for the harmonic map flow in two dimensions

  • Alexandre Freire
Article

Abstract

LetM be a two-dimensional Riemannian manifold with smooth (possibly empty) boundary. Ifu andv are weak solutions of the harmonic map flow inH1(M×[0,T]; SN) whose energy is non-increasing in time and having the same initial data u0 ε H1(M,SN) (and same boundary values γ εH3/2(∂M; SN) if ∂M; SN ≠Ø) thenu=v.

Mathematics subject classification

35K55 58E20 58G11 (1991) 

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

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

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