Interior and Boundary-Regularity for Fractional Harmonic Maps on Domains

Abstract

We prove continuity on domains up to the boundary for n/2-polyharmonic maps into manifolds. Technically, we show how to adapt Helein's direct approach to the fractional setting. This extends a remark by the author that this is possible in the setting of Riviere's famous regularity result for critical points of conformally invariant variational functionals. Moreover, pointwise behavior for the involved three-commutators is established. Continuity up to the boundary is then obtained via an adaption of Hildebrandt and Kaul's technique to the non-local setting.

References in corpus (3)

• Regularity of n/2-harmonic maps into spheres
• Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps
• 3-Commutators Estimates and the Regularity of 1/2 Harmonic Maps into Spheres

Cited by in corpus (6)

• Regularity of n/2-harmonic maps into spheres
• Sharp commutator estimates via harmonic extensions
• Hard analysis meets critical knots (Stationary points of the Moebius energy are smooth)
• ε-regularity for systems involving non-local, antisymmetric operators
• n/p-Harmonic maps: regularity for the sphere case
• Three examples of Sharp Commutator Estimates via Harmonic Extensions