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 $D$.