2017
Том 69
№ 9

All Issues

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

Sevost'yanov E. A.


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 $D$.

Citation Example: Sevost'yanov E. A. On the equicontinuity of mappings with branching in the closure of the domain // Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 273-279.