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On boundary-non-preserving mappings with Poletsky inequality

Part of: Two-dimensional theory Geometric function theory Higher-dimensional theory

Published online by Cambridge University Press:  03 February 2025

Victoria Desyatka  and
Evgeny Sevost’yanov Open the ORCID record for Evgeny Sevost’yanov [Opens in a new window]
Victoria Desyatka
Affiliation:
Department of Mathematical Analysis, Business Analysis and Statistics of Zhytomyr Ivan Franko State University, 40 Velyka Berdychivs’ka Str., 10 008 Zhytomyr, Ukraine e-mail: [email protected]
Evgeny Sevost’yanov*
Affiliation:
Department of Mathematical Analysis, Business Analysis and Statistics of Zhytomyr Ivan Franko State University, 40 Velyka Berdychivs’ka Str., 10 008 Zhytomyr, Ukraine and Department of Function Theory of Institute of Applied Mathematics and Mechanics of NAS of Ukraine, 19 Henerala Batyuka Str., 84 116 Slov’yans’k, Ukraine
*
e-mail: [email protected]
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Abstract

The manuscript is devoted to the boundary behavior of mappings with bounded and finite distortion. We consider mappings of domains of the Euclidean space that satisfy weighted Poletsky inequality. Assume that, the definition domain is finitely connected on its boundary and, in addition, on the set of all points which are pre-images of the cluster set of this boundary. Then the specified mappings have a continuous boundary extension provided that the majorant in the Poletsky inequality satisfies some integral divergence condition, or has a finite mean oscillation at every boundary point.

Keywords

Quasiconformal mappingsquasiregular mappingsmappings with finite distortionboundary behavior

MSC classification

Primary: 30C65: Quasiconformal mappings in $^n$, other generalizations 31A15: Potentials and capacity, harmonic measure, extremal length 31B25: Boundary behavior
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 22
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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