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Existence and partial regularity results for the heat flow for harmonic maps. (English) Zbl 0652.58024
For $$M={\mathbb{R}}^ m$$or compact m-dimensional manifolds M, $$m>2$$, and compact n-dimensional target manifolds N we establish the existence of a global, partially regular solution to the evolution problem (1.6-7) for harmonic maps from M into N. The solution is smooth off a singular set of co-dimension $$\geq 2$$ and as $$t\to \infty$$ converges to a partially regular harmonic map from M into N.
Reviewer: M.Struwe

##### MSC:
 58E20 Harmonic maps, etc. 58J35 Heat and other parabolic equation methods for PDEs on manifolds
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##### References:
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