Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2014, Number 5, Pages 29–35 (Mi vmumm346)  
Mathematics

Boundary behavior of derivatives of conformal mappings of simply connected domains

E. P. Dolzhenkoa, S. V. Kolesnikovb

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Ivanovo State Power University
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Abstract: Conformal mappings of simply connected domains $G$ on a disc or a halfplane are considered in the case when boundaries consist of smooth boundary arcs $\Gamma$ reachable from inside of $G$. Sufficient conditions for existence of angular limit of the derivative of such mappings and its boundedness at some given boundary point are found. A sufficient condition of existence of a bounded derivative on the region's boundary is given as a corollary.
Key words: conformal maps, angular limit, Lipschitz's condition.
Received: 19.04.2013
English version:
Moscow University Mathematics Bulletin, 2014, Volume 69, Issue 5, Pages 205–210
DOI: https://doi.org/10.3103/S0027132214050052
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: E. P. Dolzhenko, S. V. Kolesnikov, “Boundary behavior of derivatives of conformal mappings of simply connected domains”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, no. 5, 29–35; Moscow University Mathematics Bulletin, 69:5 (2014), 205–210
Citation in format AMSBIB
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\paper Boundary behavior of derivatives of conformal mappings of simply connected domains
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
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\issue 5
\pages 29--35
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\jour Moscow University Mathematics Bulletin
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