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

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 Schrödinger type equation with a 3-terms commutators in the right-hand-side . We then establish a sharp estimate for these 3-commutators.

53 p. (new commutator estimates)

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• Regularity of n/2-harmonic maps into spheres
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• Compactness and Bubbles Analysis for 1/2-harmonic Maps
• A Pohozaev-type formula and Quantization of Horizontal Half-Harmonic Maps
• Sub-criticality of Schroedinger Systems with Antisymmetric Potentials
• The obstacle problem for nonlinear integro-differential operators
• Nonlocal Harnack inequalities