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

2009/01/16 by Francesca Da Lio, Da Lio, Francesca, Tristan Rivière +1 · 1 citation
Mathematics · #35B65 #35J20 #35J60 #35S99 #58E20 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0901.2533

openalex publication_date 2009/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Weak solutions and development of singularities of the SU(2) σ‐model

Cited by

• The obstacle problem for nonlinear integro-differential operators

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