Calculus of Variations and Geometric Measure Theory

C. Mora-Corral - A. Pratelli

Approximation of piecewise affine homeomorphisms by diffeomorphisms

created by pratelli on 12 Sep 2012
modified on 16 Feb 2015


Published Paper

Inserted: 12 sep 2012
Last Updated: 16 feb 2015

Journal: J. Geom. Anal.
Year: 2012


We prove that any countably piecewise affine homeomorphism from an open set of $\mathbb{R}^2$ can be approximated, together with its inverse, by diffeomorphisms in the $W^{1,p}$ and the $L^{\infty}$ norms.