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 map**s with bounded Dirichlet integral and establish the equicontinuity and normality of the families of inverse map**s.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 9, pp. 1254–1265, September, 2013.
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Ryazanov, V.I., Salimov, R.R. & Sevost’yanov, E.A. On the Orlicz–Sobolev Classes and Map**s with Bounded Dirichlet Integral. Ukr Math J 65, 1394–1405 (2014). https://doi.org/10.1007/s11253-014-0867-1
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DOI: https://doi.org/10.1007/s11253-014-0867-1