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Problemy Analiza — Issues of Analysis, 2019, Volume 8(26), Issue 3, Pages 147–151
DOI: https://doi.org/10.15393/j3.art.2019.6670 (Mi pa280) 		 
On the compactness of one class of quasiconformal mappings

E. A. Shcherbakov, I. A. Avdeyev

Kuban State University, 149 Stavropolskaya str., Krasnodar 350040, Russia
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DOI: https://doi.org/10.15393/j3.art.2019.6670
Abstract: We consider an elliptic system in the disk ${|z|<1}$ for the so-called $p$-analytic functions. This system admits degeneration at the boundary of the disk. We prove compactness of the family of $K$-quasiconformal mappings, which are the solutions of the uniformly elliptic systems approximating the degenerating one.
Keywords: quasi-conformal mappings, sobolev spaces, elliptic systems, embedding theorems, topological mappings, Dirichlet integral, Douglas integral, harmonic functions.
Received: 09.07.2019
Revised: 30.10.2019
Accepted: 29.10.2019
Bibliographic databases:
Document Type: Article
UDC: 517.3
MSC: 30C70, 30C75
Language: English
Citation: E. A. Shcherbakov, I. A. Avdeyev, “On the compactness of one class of quasiconformal mappings”, Probl. Anal. Issues Anal., 8(26):3 (2019), 147–151
Citation in format AMSBIB
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\by E.~A.~Shcherbakov, I.~A.~Avdeyev
\paper On the compactness of one class of quasiconformal mappings
\jour Probl. Anal. Issues Anal.
\yr 2019
\vol 8(26)
\issue 3
\pages 147--151
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\crossref{https://doi.org/10.15393/j3.art.2019.6670}
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\elib{https://elibrary.ru/item.asp?id=41470788}
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