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

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 certa...

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Bibliographic Details
Published inUkrainian mathematical journal Vol. 69; no. 11; pp. 1821 - 1834
Main Authors Sevost’yanov, E. A., Petrov, E. A.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2018
Springer
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Boundaries
Geometry
Mathematics
Mathematics and Statistics
Statistics
Stretching
Theorems
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Summary: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.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-018-1472-5