Regularity and Uniqueness of p-harmonic Maps with Small Range

TL;DR

This paper proves the uniqueness and regularity of p-harmonic maps with small-range images, extending known results for harmonic maps and demonstrating that such maps have Hölder continuous derivatives.

Contribution

It establishes the uniqueness and regularity of p-harmonic maps with small images, extending previous results for harmonic maps to the p-harmonic case.

Findings

Solutions are unique for p-harmonic maps with small-range images.

Such maps have Hölder continuous derivatives.

The results extend known harmonic map theorems to p-harmonic maps.

Abstract

We prove the uniqueness of solutions to Dirichlet problem for p-harmonic maps with images in a small geodesic ball of the target manifold. As a consequence, we show that such maps have Hoelder continuous derivatives. This gives an extension of a result by S. Hildebrandt et al concerning harmonic maps.