On the local behavior of open discrete mappings of the Orlicz – Sobolev classes

Abstract

The paper is devoted to the study of mappings with unbounded characteristic of quasiconformality and, in particular, of mappings with finite distortion extensively studied in recent years. We obtain theorems on equicontinuity of families of mappings that belong to the Orlicz–Sobolev class for $n \geq 3$, and have finite distortion. To do this, we also investigate some auxiliary classes of mappings, namely, we study the relationship between the so-called lower $Q$-mappings and some inequalities of the capacity type.