*Accepted Paper*

**Inserted:** 24 feb 2015

**Last Updated:** 1 sep 2017

**Journal:** J. Eur. Math. Soc.

**Year:** 2015

**Abstract:**

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.

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