Approximation of planar Sobolev W-2,W-1 homeomorphisms by piecewise quadratic homeomorphisms and diffeomorphisms

Abstract

Given a Sobolev homeomorphism f is an element of W-2,W-1 in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of epsilon measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms in the W-2,W-1 norm on this set.

Keywords

• Diffeomorphic approximation
• Ball-Evan's
• Sobolev homeomorphism