Smooth homeomorphic approximation of piecewise affine homeomorphisms

Abstract

Given any $f$ a locally finitely piecewise affine homeomorphism of $Ω\subset \rn$ onto $Δ\subset \rn$ in $W^{1,p}$, $1\le p<\infty$ and any $\epsilon >0$ we construct a smooth injective map $\tilde{f}$ such that $\|f-\tilde{f}\|_{W^{1,p}(Ω,\rn)} < ε$.

20 pages, 1 figure