arXiv subjects

Oleksandr Dovhopiatyi

Publications and source records attributed to Oleksandr Dovhopiatyi.

6 recordsLinked to original sources

arXiv2026

On boundary non-preserving mappings with integral constraints

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.

math.CV↗

arXiv2023

On boundary Hölder logarithmic continuity of mappings in some domains

We study mappings satisfying some estimate of distortion of modulus of families of paths. Under some conditions on definition and mapped domains, we have proved that these mappings are logarithmic Hölder continuous at boundary points.

math.CV↗

arXiv2022

On boundary extension of mappings of Riemannian surfaces in terms of prime ends

We investigate non-homeomorphic mappings of Riemannian surfaces of Sobolev class. We have obtained some estimates of distortion of moduli of families of curves. We have proved that, under some conditions, these mappings have a continuous extension to a boundary of a domain in terms of prime ends.

math.CV↗

arXiv2022

On the inverse $K_I$-inequality for one class of mappings

We study mappings differentiable almost everywhere, possessing the $N$-Luzin property, the $ N^{\,-1}$-property on the spheres with respect to the $(n-1)$-dimensional Hausdorff measure and such that the image of the set where its Jacobian equals to zero has a zero Lebesgue measure. It is proved that such mappings satisfy the lower bound for the Poletsky-type distortion in their domain of definition.

math.CV↗

arXiv2022

On Beltrami equations with the inverse conditions and hydrodynamic normalization

We consider problems concerning the existence of solutions of the Beltrami equations and their convergence in the entire complex plane. We are mainly interested in the case when these solutions satisfy the so-called hydrodynamic normalization condition in the neighborhood of infinity. Under conditions related to dilations of inverse mappings, we have established the existence of such solutions in the class of continuous Sobolev mappings. We have also obtained results on the locally uniform limit of a sequence of such solutions.

math.CV↗

arXiv2021

On compactness of one class of solutions of the Dirichlet problem

We consider the Dirichlet problem for the Beltrami equation in some simply connected domain. We consider the class of all homeomorphic solutions of such a problem with a normalization condition and set-theoretic constraints on their complex characteristics. We have proved the compactness of this class in terms of prime ends for an arbitrary continuous function in the Dirichlet condition.

math.CV↗