The theory of shell-based Q-mappings in geometric function theory
Zhytomyr State University Library
Переглянути архів Інформація| Поле | Співвідношення | |
| Relation |
http://eprints.zu.edu.ua/14103/
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| Title |
The theory of shell-based Q-mappings in geometric function theory |
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| Creator |
Sevost’yanov, Е. А.
Salіmov, R. R. |
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| Subject |
Mathematical Analysis
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| Description |
Open, discrete Q-mappings in Rn, n > 2, Q 2 L1 loc, are proved to be absolutely continuous on lines, to belong to the Sobolev class W1,1 loc , to be differentiable almost everywhere and to have the N−1-property (converse to the Luzin N-property). It is shown that a family of open, discrete shell-based Q-mappings leaving out a subset of positive capacity is normal, provided that either Q has finite mean oscillation at each point or Q has only logarithmic singularities of order at most n − 1. Under the same assumptions on Q it is proved that an isolated singularity x0 2 D of an open discrete shell-based Q-map f : D \ {x0} ! Rn is removable; moreover, the extended map is open and discrete. On the basis of these results analogues of the well-known Liouville, Sokhotskii-Weierstrass and Picard theorems are obtained. |
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| Date |
2010
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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/14103/1/Sbornik_Mathematics.pdf
Sevost’yanov, Е. А. and Salіmov, R. R. (2010) The theory of shell-based Q-mappings in geometric function theory. Mathematics Subject Classification, 201 (6). pp. 909-934. |
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