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≠O) 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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