Quasiconformal mappings and Hölder continuity

Abstract

We establish that every $K$-quasiconformal mapping $w$ of the unit ball $\IB$ onto a $C^2$-Jordan domain $\Omega$ is Hölder continuous with constant $\alpha =2-\frac{n}{p}$, provided that its weak Laplacean $\Delta w$ is in $ L^p(\IB)$ for some $n/2<p<n$. In particular it is Hölder continuous for every $0<\alpha <1$ provided that $Δw\in L^n(\IB)$.

8 pages