n/p-Harmonic maps: regularity for the sphere case

Abstract

We introduce n/p-harmonic maps as critical points of E(v) the Lp-Norm of the alpha-laplacian of v, where pointwise v maps Rn into a sphere, and alpha = n/p. This energy combines the non-local behaviour of the fractional harmonic maps introduced by Riviere and the first author with the degenerate arguments of the n-laplacian. In this setting, we will prove Holder continuity.

References in corpus (2)

• Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps
• Interior and Boundary-Regularity for Fractional Harmonic Maps on Domains

Cited by in corpus (1)

• Compactness and Bubbles Analysis for 1/2-harmonic Maps