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On the lower order of mappings with finite length distortion
E. A. Sevostyanov I. Franko Zhitomir State University, Zhitomir, Ukraine
Abstract:
We study the problem of the so-called lower order for one kind of mappings with finite distortion, actively investigated in the recent 15–20 years. We prove that mappings with finite length distortion $f:D\rightarrow \mathbb{R}^n$, $n\ge 2$, whose outer dilatation is integrable to the power $\alpha>n-1$ with finite asymptotic limit have lower order bounded from below.
Key words:
mappings with bounded and finite distortion, growth of a mapping at infinity, open discrete mapping, capacity of a condenser.
Received: 18.05.2014
Citation:
E. A. Sevostyanov, “On the lower order of mappings with finite length distortion”, Mat. Tr., 18:1 (2015), 98–117; Siberian Adv. Math., 26:2 (2016), 126–138
Linking options:
https://www.mathnet.ru/eng/mt287 https://www.mathnet.ru/eng/mt/v18/i1/p98
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