Abstract
LetM be a two-dimensional Riemannian manifold with smooth (possibly empty) boundary. Ifu andv are weak solutions of the harmonic map flow inH 1(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 εH 3/2(∂M; SN) if ∂M; SN ≠Ø) thenu=v.
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Freire, A. Uniqueness for the harmonic map flow in two dimensions. Calc. Var 3, 95–105 (1995). https://doi.org/10.1007/BF01190893
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DOI: https://doi.org/10.1007/BF01190893