QCH mappings between unit ball and domain with $C^{1,\alpha}$ boundary

Abstract

We prove the following. If $f$ is a harmonic quasiconformal mapping between the unit ball in $\mathbb{R}^n$ and a spatial domain with $C^{1,\alpha}$ boundary, then $f$ is Lipschitz continuous in $B$. This generalizes some known results for $n=2$ and improves some others in higher dimensional case.