Ukrainian Mathematical Journal

, Volume 65, Issue 9, pp 1394–1405 | Cite as

On the Orlicz–Sobolev Classes and Mappings with Bounded Dirichlet Integral

  • V. I. Ryazanov
  • R. R. Salimov
  • E. A. Sevost’yanov

It is shown that homeomorphisms f in \( {{\mathbb{R}}^n} \), n ≥ 2, with finite Iwaniec distortion of the Orlicz–Sobolev classes W 1,φ loc under the Calderon condition on the function φ and, in particular, the Sobolev classes W 1,φ loc, p > n - 1, are differentiable almost everywhere and have the Luzin (N) -property on almost all hyperplanes. This enables us to prove that the corresponding inverse homeomorphisms belong to the class of mappings with bounded Dirichlet integral and establish the equicontinuity and normality of the families of inverse mappings.


Carnot Group Sobolev Class Total Differential Coordinate Hyperplane Ordinary Partial Derivative 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • V. I. Ryazanov
    • 1
  • R. R. Salimov
    • 1
  • E. A. Sevost’yanov
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian National Academy of SciencesDonetskUkraine

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