Diffeomorphic approximation of Sobolev homeomorphisms

TL;DR

This paper proves that Sobolev homeomorphisms between planar open sets can be approximated by diffeomorphisms within the same Sobolev space, enhancing understanding of their structure and approximation properties.

Contribution

It establishes the approximation of Sobolev homeomorphisms by diffeomorphisms in the Sobolev norm for the first time in the planar case.

Findings

Sobolev homeomorphisms are approximable by diffeomorphisms

Approximation holds in the Sobolev norm for 1<p<ty

Results contribute to geometric analysis and topology of Sobolev mappings

Abstract

Every homeomorphism h : X -> Y between planar open sets that belongs to the Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm by diffeomorphisms.