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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



On spatial mappings with integral restrictions on the characteristic

Author: E. A. Sevost′yanov
Translated by: E. Dubtsov
Original publication: Algebra i Analiz, tom 24 (2012), nomer 1.
Journal: St. Petersburg Math. J. 24 (2013), 99-115
MSC (2010): Primary 30C65
Published electronically: November 15, 2012
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Abstract: For a given domain $ D\subset {\mathbb{R}}^n$, some families $ {\mathfrak{F}}$ of mappings $ f\,:\,D\rightarrow \overline {{\mathbb{R}}^n}$, $ n\ge 2$ are studied; such families are more general than the mappings with bounded distortion. It is proved that a family is equicontinuous if $ \int _{\delta _0}^{\infty } \frac {d\tau }{\tau [\Phi ^{-1}(\tau )]^{\frac {1}{n-1}}}= \infty $, where the integral depends on each mapping $ f\in {\mathfrak{F}}$, $ \Phi $ is a special function, and $ \delta _0>0$ is fixed. Under similar restrictions, removability results are obtained for isolated singularities of $ f$. Also, analogs of the well-known Sokhotsky-Weierstrass and Liouville theorems are proved.

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Additional Information

E. A. Sevost′yanov
Affiliation: Institute of Applied Mathematics and Mechanics, Rozy Luxembourg str. 74, Donetsk 83114, Ukraine

Keywords: Spatial mappings, capacity, integral restrictions
Received by editor(s): November 25, 2010
Published electronically: November 15, 2012
Article copyright: © Copyright 2012 American Mathematical Society

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