On the equicontinuity of mappings with branching in the closure of the domain

Abstract

We study the problem of local behavior of mappings f : D \rightarrow R^n,\; n \geq 2,$in$D$. Under certain conditions imposed on a measurable function$Q(x), Q : D \rightarrow [0,\infty ]$, and the boundaries of$D$and$D\prime = f(D)$, we show that a family of open discrete mappings$f : D \rightarrow R^n$with a characteristic of quasiconformality$Q(x)$is equicontinuous in$D$.