$ACL$ and differentiability of the Open Discrete Ring (p,Q)-Mappings

Abstract

We study the so--called ring $(p,Q)$--mappings which are the natural generalization of quasiregular and quasi isometric mappings. It is proved that open discrete ring $(p,Q)$--mappings are differentiable a.e. and belong to the class $ACL$ in ${\Bbb R}^n$, $n\ge 2$, furthermore, $f\in W_{loc}^{1,1}$ provided that $Q\in L^{1}_{loc}$ and $p>n-1$