  We establish that every $K$-quasiconformal mapping $w$ of the unit ball $\IB$
onto a $C^2$-Jordan domain $\Omega$ is H\"older 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 H\"older continuous for every
$0<\alpha<1$ provided that $\Delta w\in L^n(\IB)$.
