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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 1, Pages 423–432
DOI: https://doi.org/10.33048/semi.2021.18.029 (Mi semr1370) 		 
Real, complex and functional analysis

A version of Schwarz's lemma for mappings with weighted bounded distortion

M. V. Tryamkin

Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2021.18.029
Abstract: We consider the class of mappings generalizing qusiregular mappings. Every mapping from this class is defined in a domain of Euclidean $n$-space and possesses the following properties: it is open, continuous, and discrete, it belongs locally to the Sobolev class $W^{1}_{q}$, it has finite distortion and nonnegative Jacobian, and its function of weighted $(p,q)$-distortion is integrable to a certian power depending on $p$ and $q$, where $n-1<q\leqslant p<\infty$. We obtain an analog of Schwarz's lemma for such mappings provided that $p\geqslant n$. The technique used is based on the spherical symmetrization procedure and the notion of Grötzsch condenser.
Keywords: capacitary estimates, Grötzsch condenser, mappings with weighted bounded distortion, Schwarz's lemma, spherical symmetrization.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0006
The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (Project no. 0314-2019-0006).
Received March 2, 2021, published April 18, 2021
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 30CX65
Language: English
Citation: M. V. Tryamkin, “A version of Schwarz's lemma for mappings with weighted bounded distortion”, Sib. Èlektron. Mat. Izv., 18:1 (2021), 423–432
Citation in format AMSBIB
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\by M.~V.~Tryamkin
\paper A version of Schwarz's lemma for mappings with weighted bounded distortion
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 1
\pages 423--432
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\crossref{https://doi.org/10.33048/semi.2021.18.029}
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