# American Institute of Mathematical Sciences

December  2018, 38(12): 6195-6214. doi: 10.3934/dcds.2018266

## Minimizing fractional harmonic maps on the real line in the supercritical regime

 1 Université Paris Diderot, Lab. J.L.Lions (CNRS UMR 7598), Paris, France 2 Johns Hopkins University, Department of Mathematics, Baltimore, USA 3 Columbia University, Department of Mathematics, New York, USA

Dedicated to Rafael de la Llave on the occasion of his 60th birthday with admiration and friendship

Received  October 2017 Revised  April 2018 Published  September 2018

This article addresses the regularity issue for minimizing fractional harmonic maps of order s∈(0, 1/2) from an interval into a smooth manifold. Hölder continuity away from a locally finite set is established for a general target. If the target is the standard sphere, then Hölder continuity holds everywhere.

Citation: Vincent Millot, Yannick Sire, Hui Yu. Minimizing fractional harmonic maps on the real line in the supercritical regime. Discrete & Continuous Dynamical Systems, 2018, 38 (12) : 6195-6214. doi: 10.3934/dcds.2018266
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