Calculus of Variations and Partial Differential Equations

, Volume 3, Issue 1, pp 95–105

Uniqueness for the harmonic map flow in two dimensions

  • Alexandre Freire
Article

DOI: 10.1007/BF01190893

Cite this article as:
Freire, A. Calc. Var (1995) 3: 95. doi:10.1007/BF01190893

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

35K5558E2058G11 (1991)

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

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