相关论文: On the local and boundary behavior of mappings on …

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…

We study the factor-spaces of the unit ball of dimension, not less than three, by a certain group of M\"{o}bius transformations. For mappings of such spaces, an estimate of the distortion of the modulus of families of spheres is obtained.…

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 H\"{o}lder inequality for such mappings, provided that their…

Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.

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…

In the present paper, we investigate non-homeomorphic mappings of Riemannian surfaces of Sobolev class. We have obtained some estimates of distortion of moduli of families of curves. As consequence, we have obtained results about the…

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…

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 H\"{o}lder continuous at boundary points.

In this paper, we obtain upper estimates for the distortion of the modulus of families of paths under mappings of the Sobolev class, whose dilatation is locally integrable. As a consequence, theorems on the local and boundary behavior of…

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…

A boundary behavior of mappings, which are closely related with Sobolev and Orlicz--Sobolev classes in the plane and in the space, is investigated. There are obtained theorems on boundary behavior of classes mentioned above.

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…

We study the automorphisms group action on a bounded domain in $\CC^n$ having a boundary point that is exponentially flat. Such a domain typically has a compact automorphism group. Our results enable us to generate many new examples.

In the present paper, it was studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions…

We explore the asymptotic behavior of families of Bourgain-Brezis-Mironescu type nonlocal functionals for mappings from metric measure spaces to arbitrary metric spaces. As the first outcome, we obtain a characterization of Sobolev maps and…

The present paper is devoted to the study of space mappings, which are more general than quasiregular mappings. The questions of the behavior of differentiable mappings having the so--called $N,$ $N^{-1},$ $ACP$ and $ACP^{-1}$ -- properties…

We consider the behavior of the nonlocal minimal surfaces in the vicinity of the boundary. By a series of detailed examples, we show that nonlocal minimal surfaces may stick at the boundary of the domain, even when the domain is smooth and…

We consider mappings that distort the modulus of families of paths in the opposite direction in the manner of Poletsky's inequality. Here we study the case when the mappings are not closed, in particular, they do not preserve the boundary…

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…

We investigate distortion estimates for mappings at boundary points of a domain. We consider mappings of the Sobolev and Orlicz-Sobolev classes and some other classes of mappings that do not preserve the boundary of a domain. For above…