Improved regularity of harmonic map flows with Hölder continuous energy

Topping, Peter
September 2004
Calculus of Variations & Partial Differential Equations;Sep2004, Vol. 21 Issue 1, p47
Academic Journal
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 Holder continuous, then the weak limit u(T) must also be Holder continuous.


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