arXiv subjects
Publications and source records attributed to N. S. Ilkevych.
We study quasilinear Beltrami equations, the complex coefficients of which depend on the unknown function. In terms of the so-called tangential dilatation, we have found conditions under which these equations have homeomorphic $ACL$-solutions. Sepa\-ra\-tely, we have found some conditions that ensure the existence of the corresponding con\-ti\-nuous $ACL$-solutions.
The article is devoted to the study of mappings that satisfy the so-called inverse Poletsky inequality. We consider mappings of quasiextremal distance domains, domains with a locally quasiconformal boundary, and domains which are regular in the sense of prime ends onto domains with a locally quasiconformal boundary, regular domains, or domains which are locally Hölder equivalent to a half-ball on its boundary. For such mappings, we have obtained the Hölder logarithmic continuity in some neighborhood of its boundary points.
We study branching mappings that satisfy some condition of distortion of the modulus of families of paths. In a situation where the definition domain of mappings is locally connected on its boundary, the mapped domain is regular, and the majorant responsible for distortion of the modulus of families of paths is integrable, it is proved that the families of all specified mappings with one normalization condition are equicontinuous in the closure of the given domain.
The paper is devoted to the study of mappings with finite distortion, actively studied recently. For mappings whose inverse satisfy the Poletsky inequality, the results on boundary behavior in terms of prime ends are obtained. In particular, it was proved that the families of the indicated mappings are equicontinuous at the points of the boundary if a certain function determining the distortion of the module under the mappings is integrable in a given domain.