Diffeomorphic Approximation of $W^{1,1}$ Planar Sobolev Homeomorphisms

Let $\mathrm{\Omega }\subseteq {\mathbb{R}}^2$ be a domain and let $f\in W^{1,1}(\Omega,\mathbb R^2)$beahomeomorphism(between$\Omega$and$f(\Omega)$)\mathrm{.}Thenthereexistsasequenceofsmoothdiffeomorphisms$f_k$convergingto$f$in$W^{1,1}(\Omega,\mathbb R^2)$ and uniformly.