Compactness Theory and Mappings with Finite Length Distortion
Zhytomyr State University Library
Переглянути архів Інформація| Поле | Співвідношення | |
| Relation |
http://eprints.zu.edu.ua/14094/
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| Title |
Compactness Theory and Mappings with Finite Length Distortion
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| Creator |
Sevost’yanov, Е. А.
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| Subject |
Mathematical Analysis
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| Description |
The present paper is devoted to the study of mappings with finite length distortion introduced in 2004 by O. Martio, V. Ryazanov, U. Srebro, and E. Yakubov. It is proved that the locally uniform limit of homeomorphisms with finite length distortion is a homeomorphism or a constant provided that the so-called inner dilatations of the sequence of homeomorphisms are almost everywhere (a.e.) majorized by a locally integrable function. In particular, it is studied the pointwise behavior of the so-called outer dilatations. For these dilatations, the pointwise semicontinuity and semicontinuty in the mean are proved. It is also proved some theorems on the convergence of matrix dilatations. It is proved that the class of homeomorphisms with finite length distortion is closed in the space of all homeomorphisms, under minimal conditions on dilatations of the direct and inverse mappings. The results of the paper can be applied to various classes of spatial mappings. |
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| Date |
2009
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| Type |
Article
PeerReviewed |
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| Format |
text
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| Language |
uk
english |
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| Identifier |
http://eprints.zu.edu.ua/14094/1/SBAM179.pdf
Sevost’yanov, Е. А. (2009) Compactness Theory and Mappings with Finite Length Distortion. Siberian Advances in Mathematics, 19 (3). pp. 179-191. ISSN 1055-1344 |
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