Diffeomorphic approximation of piecewise affine homeomorphisms

Daniel Campbell, Luigi D'Onofrio, Tomáš Vítek

Given any $f$ a locally finitely piecewise affine homeomorphism of $\Omega \subset {\mathbb{R}}^d$ onto $\Delta \subset {\mathbb{R}}^d$ (for $d=3,4$) such that $f\in W^{1,p}(\Omega ,{\mathbb{R}}^d)$ and…