Calculus of Variations - Smooth homeomorphic approximation of piecewise affine homeomorphisms

Abstract

Given any integral a locally finitely piecewise affine homeomorphism of Omega subset of R-n onto Delta subset of R-n in W-1,W-p, 1 <= p < infinity and any epsilon > 0 we construct a smooth injective map (f) over tilde such that parallel to f - (f) over tilde parallel to(W1,p (Omega, Rn)) < epsilon.