Calculus of Variations and Geometric Measure Theory

S. Hencl - A. Pratelli

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

created by pratelli on 24 Feb 2015
modified on 17 Dec 2019


Published Paper

Inserted: 24 feb 2015
Last Updated: 17 dec 2019

Journal: J. Eur. Math. Soc.
Year: 2018


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.