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arxiv: 1003.4690 · v2 · submitted 2010-03-24 · 🧮 math.CV

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

classification 🧮 math.CV
keywords mappingsringdiscreteopenbelongclassdifferentiabilitydifferentiable
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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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