On the local behavior of a class of inverse mappings

Abstract

We study the families of mappings such that the inverse ones satisfy an inequality of the Poletskii type in the given domain. It is proved that those families are equicontinuous at the inner points, if the initial and mapped domains are bounded, and the majorant responsible for a distortion of the modulus is integrable. But if the initial domain is locally connected on its boundary, and if the boundary of the mapped domain is weakly flat, then the corresponding families of mappings are equicontinuous at the inner and boundary points.