On boundary non-preserving mappings with integral constraints
Complex Variables
2026-03-03 v1
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.
Cite
@article{arxiv.2603.00969,
title = {On boundary non-preserving mappings with integral constraints},
author = {Victoria Desyatka and Oleksandr Dovhopiatyi and Evgeny Sevost'yanov},
journal= {arXiv preprint arXiv:2603.00969},
year = {2026}
}