$ACL$ and differentiability of open discrete ring $(p,Q)$-mappings

Author R. R. Salimov, E. A. Sevost’yanov
salimov@iamm.ac.donetsk.ua, brusin2006@rambler.ru
Institute of Applied Mathematics and Mechanics, Donetsk

Abstract We study the so-called $(p,Q)$-mappings which naturally generalize quasiregular mappings. It is proved that open discrete ring $(p,Q)$-mappings are differentiable almost everywhere as $p>n-1$ and locally integrable $Q.$ Furthermore, we prove that open discrete $(p,Q)$-mappings belong to the class $ACL$ in ${\Bbb R}^n$ and $f\in W_{\rm loc}^{1,1}$ the same conditions on $p$ and $Q.$
Keywords $(p,Q)$-mapping; quasiregular mappings
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Pages 28-36
Volume 35
Issue 1
Year 2011
Journal Matematychni Studii
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