  Let $\Omega\subseteq\mathbb R^2$ be a domain and let $f\in
W^{1,1}(\Omega,\mathbb R^2)$ be a homeomorphism (between $\Omega$ and
$f(\Omega)$). Then there exists a sequence of smooth diffeomorphisms $f_k$
converging to $f$ in $W^{1,1}(\Omega,\mathbb R^2)$ and uniformly.
