arXiv subjects

O. P. Dovhopiatyi

Publications and source records attributed to O. P. Dovhopiatyi.

7 recordsLinked to original sources

arXiv2023

On behavior of one class of mappings acting onto domains with a locally quasiconformal boundary

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.

math.CV↗

arXiv2023

On distortion estimates of mappings with the Poletsky condition in domains with Poincare inequality

The article is devoted to the study of mappings that distort the modulus of families of paths according to the Poletsky inequality type. At the boundary points of the domain, we have obtained an estimate of the distance distortion for such mappings provided that their characteristic has finite integral averages over the balls, and the image domain of mappings is Ahlfors regular and such that the Poincare inequality holds. The manuscript considers the cases of homeomorphisms and mappings with branching, as well as definition domains with good boundaries and domains with prime ends.

math.CV↗

arXiv2022

On mappings with hydrodynamical normalization conditions in Euclidean space

We are studying spatial mappings that satisfy some space analog of a hydrodynamical type of growth in the neighborhood of the infinity. It is proved that homeomorphisms of the specified class form equicontinuous families under some conditions on their characteristic of quasiconformality. We have also considered the problem of closeness of these classes with respect to locally uniform convergence. We have obtained corresponding results for mappings with integral constraints, as well as for classes of corresponding inverse mappings.

math.CV↗

arXiv2021

On the existence of solutions of quasilinear Beltrami equations with two characteristics

We study Beltrami-type equations with two given complex characteristics. Under certain conditions on the complex coefficients, we obtained theorems on the existence of homeomorphic $ ACL $ -solutions of this equation. In addition, for some relatively weak conditions, we obtained theorems on the existence of the corresponding continuous $ ACL $ -solutions that are loga -rith\-mi\-cally Hölder in a given domain.

math.CV↗

arXiv2020

On compact classes of solutions of the Dirichlet problem with integral restrictions

We have proved theorems on compact classes of homeomorphisms with hydrodynamic normalization that are solutions of the Beltrami equation, whose characteristics are compactly supported and satisfy certain constraints of an integral type. As a consequence, we obtained results on compact classes of solutions of corresponding Dirichlet problems considered in some Jordan domain.

math.CV↗

arXiv2020

On compactness of classes of solutions of the Dirichlet problem with restrictions of the theoretics-set type

We have proved theorems on compact classes of homeomorphisms with hydrodynamic normalization that are solutions of the Beltrami equation, whose characteristics are compactly supported and satisfy certain constraints of the theoretical-set type. As a consequence, we obtained results on compact classes of solutions of corresponding Dirichlet problems considered in some Jordan domain.

math.AP↗

arXiv2019

On mappings satisfying the inverse Poletsky inequality

We have studied the local and boundary behavior of mappings satisfying one estimate of the distortion of the modulus of families of paths. In particular, we have obtained conditions under which the families of the indicated mappings are equicontinuous inside and on the boundary of a domain.

math.CA↗