Minimizing fractional harmonic maps on the real line in the supercritical regime
Vincent Millot, Yannick Sire, Hui Yong Yu · Discrete and Continuous Dynamical Systems · 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.