On mappings with an analog of the hydrodynamical normalization in the Euclidean space

Abstract

Spatial mappings that satisfy some spatial analog of the hydrodynamic condition in the vicinity of an infinitely remote point have been studied. It has been proved that homeomorphisms of the indicated class form equicontinuous families under certain conditions on their quasi-conformity characteristic. The issue concerning the closure of those classes with respect to the locally uniform convergence has also been considered. Relevant results have been obtained for mappings with integral restrictions, as well as for classes of corresponding inverse mappings.