Bisobolev mappings and homeomorphisms with finite distortion

Abstract

Let $\Omega$ and ${\Omega }^{\prime }$ be bounded open sets in ${\mathbb{R}}^n,n\ge 2$, and let $\mathrm{Hom}(\Omega ;{\Omega }^{\prime })$ the class of homeomorphisms $f:\Omega \to {\Omega }^{\prime }$. We illustrated some properties of bisobolev homeomorphisms and their connections with homeomorphisms with finite distortion.