On the boundary behavior of open discrete mappings with unbounded characteristic

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.