Geodesic
A version of Schwarz's lemma for mappings with weighted bounded distortion
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 423-432

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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 $n-1$. 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, mappings with weighted bounded distortion, Schwarz's lemma, spherical symmetrization.
Mots-clés : Grötzsch condenser 
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     author = {M. V. Tryamkin},
     title = {A version of {Schwarz's} lemma for mappings with weighted bounded distortion},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     publisher = {mathdoc},
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     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a45/}
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M. V. Tryamkin. A version of Schwarz's lemma for mappings with weighted bounded distortion. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 423-432. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a45/