2017
Том 69
№ 9

All Issues

On the boundary behavior of open discrete mappings with unbounded characteristic

Sevost'yanov E. A.

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Abstract

We study the problem of extension of mappings $f : D → R^n,\; n ≥ 2$, to the boundary of a domain $D$. Under certain conditions imposed on a measurable function $Q(x),\; Q: D → [0, ∞]$, and the boundaries of the domains $D$ and $D' = f(D)$, we show that an open discrete mapping $f : D → R^n,\; n ≥ 2$, with quasiconformality characteristic $Q(x)$ can be extended to the boundary $\partial D$ by continuity. The obtained statements extend the corresponding Srebro’s result to mappings with bounded distortion.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 6, pp 979-984.

Citation Example: Sevost'yanov E. A. On the boundary behavior of open discrete mappings with unbounded characteristic // Ukr. Mat. Zh. - 2012. - 64, № 6. - pp. 855-859.

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