On the boundary behavior of open discrete mappings with unbounded characteristic - Sevost'yanov, E. A. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
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 D by continuity. The obtained statements extend the corresponding Srebro’s result to mappings with bounded distortion.