improved regularity of harmonic map flows with hölder continuous energy ∗
نویسنده
چکیده
For a smooth harmonic map flow u : M× [0, T ) → N with blow-up as t ↑ T , it has been asked ([6], [5], [7]) whether the weak limit u(T ) : M→ N is continuous. Recently, in [12], we showed that in general it need not be. Meanwhile, the energy function E(u(·)) : [0, T ) → R, being weakly positive, smooth and weakly decreasing, has a continuous extension to [0, T ]. Here we show that if this extension is also Hölder continuous, then the weak limit u(T ) must also be Hölder continuous.
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