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.
3-Commutators Estimates and the Regularity of 1/2-Harmonic Maps into Spheres,
DA LIO, FRANCESCA;
2011
Abstract
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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