On boundary non-preserving mappings with integral constraints

TL;DR

This paper investigates boundary non-preserving mappings that satisfy weighted Poletsky inequalities with integral constraints, establishing conditions under which these mappings are equicontinuous up to the boundary.

Contribution

It introduces new conditions involving integral constraints and boundary behavior that ensure equicontinuity of such mappings.

Findings

Mappings are equicontinuous under specified conditions.

Boundary non-preserving mappings can be controlled with integral constraints.

The results extend understanding of boundary behavior in weighted inequalities.

Abstract

This manuscript is devoted to the study of mappings, satisfying the upper weighted Poletsky inequality. We study the case where the boundary of the domain may not be preserved under the mapping and, besides that, the majorant from the above inequality satisfies constraints of the integral-type. Under certain additional conditions on the definition domain and the corresponding cluster sets, we prove that families of above mappings are equicontinuous in the closure of this domain.