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E. A. Sevost'yanov

Publications and source records attributed to E. A. Sevost'yanov.

At least 19 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

Removable singularities of mappings with inverse Poletksy inequality on Rie\-man\-nian manifolds

We consider open discrete mappings of Riemannian manifolds that satisfy some modulus inequality. We investigate the possibility of a continuous extension of such mappings to an isolated point on the boundary. It is proved that, these mappings have a specified extension, if they omit two or more points of a connected Riemannian manifold, and the majorant participating in the modulus inequality is integrable over almost all spheres.

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↗
arXiv2023

On mappings with the inverse Poletsky inequality on Riemannian surfaces

We study some problems related to the boundary behavior of maps of domains of Riemannian surfaces. In particular, for mappings satisfying the inverse Poletsky type modulus inequality, we establish the possibility of their continuous extension to the boundary in terms of prime ends. We also study the local behavior of such mappings at boundary points.

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↗
arXiv2022

On modulus inequality of the order $p$ for the inner dilatation

The article is devoted to mappings with bounded and finite distortion of plane domains. Our investigations are devoted to the connection between mappings of the Sobolev class and upper bounds for the distortion of the modulus of families of paths. For this class, we have proved the Poletsky-type inequality with respect to the so-called inner dilatation of the order~$p.$ Along the way, we also obtained lower bounds for the modulus distortion under mappings. We separately considered the situations of homeomorphisms and mappings with branch points.

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 logarithmic Holder continuity of mappings on the boundary

We study mappings satisfying the so-called inverse Poletsky inequality. Under integrability of the corresponding majorant, it is proved that these mappings are logarithmic Hölder continuous in the neighborhood of the boundary points. In particular, the indicated properties hold for homeomorphisms whose inverse satisfy the weighted Poletsky inequality.

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↗
arXiv2020

Equicontinuity by the prime ends of mappings with the normalization condition

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.

math.CV↗
arXiv2019

On equicontinuity of families of mappings with a fixed point of a domain

The behavior of a class of mappings of a domain of Euclidean space is studied. It is established that the indicated class is equicontinuous both at the inner and at the boundary points of the domain if the mappings contained in it satisfy the general normalization condition, and the corresponding characteristic of quasiconformality has a weak growth.

math.MG↗
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↗
arXiv2019

On behavior of a class of mappings in terms of prime ends

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.

math.CV↗
arXiv2018

On behavior of homeomorphisms with inverse modulus conditions

We consider some class of homeomorphisms of domains of Euclidean space, which are more general than quasiconformal mappings. For these homeomorphisms, we have obtained theorems on local behavior of it's inverse mappings in a given domain. Under some additional conditions, we proved results about behavior of mappings mentioned above in the closure of the domain.

math.MG↗