2017
Том 69
№ 9

All Issues

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

Ryazanov V. I., Salimov R. R., Sevost'yanov E. A.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 9, pp 1394-1405.

Citation Example: Ryazanov V. I., Salimov R. R., Sevost'yanov E. A. On the Orlicz–Sobolev Classes and Mappings with Bounded Dirichlet Integral // Ukr. Mat. Zh. - 2013. - 65, № 9. - pp. 1254–1265.

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