Bisobolev mappings and homeomorphisms with finite distortion

Abstract

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