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

• Date: 2017
• Main Authors: Sevost'yanov, E. A., Севостьянов, Е. А.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2017
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1693
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 \...