3-Commutators Estimates and the Regularity of 1/2 Harmonic Maps into Spheres

Mathematics – Analysis of PDEs

Scientific paper

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53 p. (new commutator estimates)

Scientific paper

We prove the regularity of weak 1/2-harmonic maps from the real line into a
sphere. The key point in our result is first a formulation of the 1/2-harmonic
map equation in the form of a non-local linear Schr\"odinger type equation with
a 3-terms commutators in the right-hand-side . We then establish a sharp
estimate for these 3-commutators.

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