Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 199, Pages 80–85
DOI: https://doi.org/10.36535/0233-6723-2021-199-80-85 (Mi into892) 		 
Differential properties of mappings with $s$-average characteristic

A. N. Malyutinaa, U. K. Asanbekovb, A. V. Novikb

a Tomsk State University, Faculty of Mechanics and Mathematics
b Tomsk State University
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DOI: https://doi.org/10.36535/0233-6723-2021-199-80-85
Abstract: In this paper, we develop the geometric method of moduli of curve families and consider the problem of differential properties of nonhomeomorphic mappings with $s$-averaged characteristic. These properties can be applied in the theory of multidimensional quasiconformal mappings and their generalizations. We prove that if $f$ is an extremal mapping with $s$-averaged characteristic, then it belongs to the class $W^2_2$.
Keywords: homeomorphism, mapping, characteristic, distortion, module of a family of curves.
Document Type: Article
UDC: 517.54
MSC: 26B30, 26B35
Language: Russian
Citation: A. N. Malyutina, U. K. Asanbekov, A. V. Novik, “Differential properties of mappings with $s$-average characteristic”, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 199, VINITI, Moscow, 2021, 80–85
Citation in format AMSBIB
\Bibitem{MalAsaNov21}
\by A.~N.~Malyutina, U.~K.~Asanbekov, A.~V.~Novik
\paper Differential properties of mappings with $s$-average characteristic
\inbook Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 --- February 1, 2020. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 199
\pages 80--85
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into892}
\crossref{https://doi.org/10.36535/0233-6723-2021-199-80-85}
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