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

  • V. I. Ryazanov Ин-т прикл. математики и механики НАН Украины, Донецк
  • R. R. Salimov Ин-т прикл. математики и механики НАН Украины, Донецк
  • E. A. Sevost'yanov

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.
Published
25.09.2013
How to Cite
RyazanovV. I., SalimovR. R., and Sevost’yanovE. A. “On the Orlicz–Sobolev Classes and Mappings With Bounded Dirichlet Integral”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 9, Sept. 2013, pp. 1254–1265, http://umj.imath.kiev.ua/index.php/umj/article/view/2506.
Section
Research articles