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

2010/03/24 by R. Salimov, Salimov, R., E. Sevostyanov +1
Mathematics · #30C65 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30C65

paper · pdf · doi:10.48550/arxiv.1003.4690

8 pages

arxiv created 2010/04/14 · arxiv updated 2010/04/19

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 Rⁿ, n≥ 2, furthermore, f∈ W_loc^1,1 provided that Q∈ L¹_loc and p>n-1

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