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Ukrainian Mathematical Journal

, Volume 69, Issue 11, pp 1821–1834 | Cite as

On the Equicontinuity of Homeomorphisms of Orlicz and Orlicz–Sobolev Classes in the Closure of a Domain

  • E. A. Sevost’yanov
  • E. A. Petrov
Article
  • 7 Downloads

We study the behavior of homeomorphisms of Orlicz–Sobolev classes in the closure of a domain. The theorems on equicontinuity of the indicated classes are obtained in terms of the prime ends of regular domains. In particular, it is shown that indicated classes are equicontinuous in domains with certain restrictions imposed on their boundaries provided that the corresponding inner dilatation of order p has a majorant of finite mean oscillation at every point. We also prove theorems on the (pointwise) equicontinuity of the analyzed classes in the case of locally connected boundaries.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • E. A. Sevost’yanov
    • 1
  • E. A. Petrov
    • 2
  1. 1.Franko Zhitomir State UniversityZhitomirUkraine
  2. 2.Institute of Applied Mathematics and MechanicsUkrainian National Academy of SciencesSlavyanskUkraine

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