On equicontinuity of homeomorphisms of the Orlicz and Orlicz – Sobolev classes in the closure of a domain
We investigate the behavior of homeomorphisms of the 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 domain...
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| Date: | 2017 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2017
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1803 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We investigate the behavior of homeomorphisms of the 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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