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Journal of the European Mathematical Society

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Volume 20, Issue 3, 2018, pp. 597–656
DOI: 10.4171/JEMS/774

Published online: 2018-02-09

Diffeomorphic approximation of $W^{1,1}$ planar Sobolev homeomorphisms

Stanislav Hencl[1] and Aldo Pratelli[2]

(1) Charles University, Prague, Czechia
(2) Universität Erlangen-Nürnberg, Erlangen, Germany

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.

Keywords: Mapping of finite distortion, approximation

Hencl Stanislav, Pratelli Aldo: Diffeomorphic approximation of $W^{1,1}$ planar Sobolev homeomorphisms. J. Eur. Math. Soc. 20 (2018), 597-656. doi: 10.4171/JEMS/774