On the boundary behavior of open discrete mappings with unbounded characteristic

  • E. A. Sevost'yanov

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.
Published
25.06.2012
How to Cite
Sevost’yanovE. A. “On the Boundary Behavior of Open Discrete Mappings With Unbounded Characteristic”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 6, June 2012, pp. 855-9, http://umj.imath.kiev.ua/index.php/umj/article/view/2623.
Section
Short communications