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

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

2010-03-24

arxiv.org/abs/1003.4690v2

Mathematics

Complex Variables

8 pages

Scientific paper

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 $p>n-1$

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