Searcharxiv⌕ Search

arXiv subjects

Evgeny Sevost'yanov

Publications and source records attributed to Evgeny Sevost'yanov.

At least 37 records · Page 2Linked to original sources
arXiv2023

On isolated singularities of mappings with inverse moduli inequalities

We consider open discrete mappings that satisfy the modulus condition of the inverse Poletsky inequality type. We study the case when the majorant in it is integrable, or more generally, has finite averages over infinitesimal spheres. We proved that such mappings have a continuous extension to an isolated point of the boundary of some domain without any a priori requirements on the corresponding mapped domain for integrable majorants. In the case of majorants, integrable on spheres, we require only the boundedness of the mapped domain. We do not require any other topological conditions on the mappings.

math.CV↗
arXiv2023

On the theory of generalized quasiconformal mappings

We study generalized quasiconformal mappings in the context of the inverse Poletsky inequality. We consider the local behavior and the boundary behavior of mappings with the inverse Poletsky inequality. In particular, we obtain logarithmic Hölder continuity for such classes of mappings.

math.CV↗
arXiv2023

On boundary Hölder continuity of mappings with the Poletsky condition

The article is devoted to the study of mappings that distort the modulus of families of paths by the Poletsky inequality type. At boundary points of a domain, we have obtained the Hölder inequality for such mappings, provided that their characteristic has finite integral averages over infinitesimal balls. In the manuscript, we have separately considered the cases of homeomorphisms and mappings with branching. Also, we have separately considered good boundaries and domains with prime ends.

math.CV↗
arXiv2022

On the boundary behavior of weak $(p,q)$-quasiconformal mappings

Let $Ω$ and $\widetildeΩ$ be domains in the Euclidean space $\mathbb R^n$. We study the boundary behavior of weak $(p,q)$-quasiconformal mappings, $φ:Ω\to \widetildeΩ$, $n-1<q\leq p<n$. The suggested method is based on the capacitary distortion properties of the weak $(p,q)$-quasiconformal mappings.

math.AP↗
arXiv2022

On discrete boundary extension of mappings in terms of prime ends

We study mappings that satisfy the inverse Poletsky inequality in a domain of the Euclidean space. Under certain conditions on the definition and mapped domains, it is established that they have a continuous extension to the boundary in terms of prime ends if the majorant involved in the Poletsky inequality is integrable over spheres. Under some additional conditions, the extension mentioned above is discrete.

math.CV↗
arXiv2022

On the inverse Poletsky inequality with cotangent dilatation

The article is devoted to establishing the distortion of the modulus of families of paths in wide classes of mappings that admit branch points. In particular, for mappings that are differentiable almost everywhere and have $N$- and $N^{\,- 1}$-Luzin properties and are absolutely continuous on almost all paths, we obtained the inverse Poletsky inequality with the so-called cotangent dilatation. We have proved that, for inverse mappings, this dilatation coincides with the so-called tangential dilatation of the corresponding inverse mapping. In addition, we have proved that cotangent dilatation is less than the outher or inner dilatation, in particular, may be less than one on the set of positive Lebesgue measure

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

Composition operators on Sobolev spaces and weighted moduli inequalities

In this paper we study connections between composition operators on Sobolev spaces and mappings defined by $p$-moduli inequalities ($p$-capacity inequalities). We prove that weighted moduli inequalities lead to composition operators on corresponding Sobolev spaces and inverse, composition operators on Sobolev spaces imply weighted moduli inequalities.

math.AP↗
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↗
arXiv2021

On the inverse Poletskii inequality in metric spaces and prime ends

We study mappings defined in the domain of a metric space that distort the modulus of families of paths by the type of the inverse Poletskii inequality. Under certain conditions, it is proved that such mappings have a continuous extension to the boundary of the domain in terms of prime ends. Under some additional conditions, the families of such mappings are equicontinuous in the closure of the domain with respect to the space of prime ends.

math.CV↗
arXiv2021

On nonhomeomorphic mappings between Riemannian manifolds

We consider mappings of domains of Riemannian manifolds that admit branch points and satisfy a certain condition regarding the distortion of the modulus of families of paths. We have established logarithmic estimates of distance distortion under such mappings. A separate study relates to the situation when the mappings are defined in metric spaces, and one of them is the Loewner space. We also studied the question of equicontinuity of the families of the indicated mappings in the closure of the domain. In addition, we have established the possibility of continuous extension of these mappings to an isolated point of the boundary.

math.CV↗
arXiv2021

On global behavior of mappings with integral constraints

This article is devoted to the study of mappings with branch points whose characteristics satisfy integral-type constraints. We have proved theorems concerning their local and global behavior. In particular, we established the equicontinuity of families of such mappings inside their definition domain, as well as, under additional conditions, equicontinuity of the families of these mappings in its closure.

math.CV↗
arXiv2020

Isolated singularities of mappings with the inverse Poletski inequality

We study open-closed discrete mappings that satisfy the weighted estimate of the distortion of modulus of families of paths. It is proved that the mappings mentioned above have a continuous extension into the isolated point of the boundary, provided that the corresponding weight function is integrable, and the cluster set of the mapping at a given point belongs to the boundary of the image under the mapping

math.CV↗