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On the power order of growth of lower $Q$-homeomorphisms
R. R. Salimov Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev
Abstract:
In the present paper we investigate the asymptotic behavior of $Q$-homeomorphisms with respect to a $p$-modulus at a point. The sufficient conditions on $Q$ under which a mapping has a certain order of growth are obtained. We also give some applications of these results to Orlicz–Sobolev classes $W^{1,\varphi}_{\mathrm{loc}}$ in $\mathbb{R}^n$, $n\geqslant 3$, under conditions of the Calderon type on $\varphi$ and, in particular, to Sobolev classes $W_{\mathrm{loc}}^{1,p},$ $p>n-1$. We give also an example of a homeomorphism demonstrating that the established order of growth is precise.
Key words:
$p$-modulus, $p$-capacity, lower $Q$-homeomorphisms, mappings of finite distortion, Sobolev class, Orlicz–Sobolev class.
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UDC:
517.5 Received: 23.10.2014
Citation:
R. R. Salimov, “On the power order of growth of lower $Q$-homeomorphisms”, Vladikavkaz. Mat. Zh., 19:2 (2017), 36–48
Citation in format AMSBIB
\Bibitem{Sal17}
\by R.~R.~Salimov
\paper On the power order of growth of lower $Q$-homeomorphisms
\jour Vladikavkaz. Mat. Zh.
\yr 2017
\vol 19
\issue 2
\pages 36--48
\mathnet{http://mi.mathnet.ru/vmj615}
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http://mi.mathnet.ru/eng/vmj615 http://mi.mathnet.ru/eng/vmj/v19/i2/p36
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