On the Local Behavior of Open Discrete Mappings from 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, which are now extensively studied. We establish theorems on the equicontinuity of the families of mappings that belong to the Orlicz–Sobolev class for n ≥ 3 and have finite distortions. To do this, we also study some auxiliary classes of mappings. In fact, we analyze the relationship between the so-called lower Q-mappings and some capacity-type inequalities.