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

TL;DR

This paper introduces n/p-harmonic maps as critical points of a fractional energy functional mapping into spheres, demonstrating their Holder continuity and blending non-local fractional harmonic map concepts with degenerate n-laplacian techniques.

Contribution

It establishes regularity results for n/p-harmonic maps into spheres, combining fractional and degenerate analysis methods in a novel way.

Findings

Proves Holder continuity of n/p-harmonic maps

Introduces a new energy functional for sphere-valued maps

Combines non-local fractional and degenerate n-laplacian techniques

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.