E. A. Sevost’yanov

Boundary behavior of Orlicz-Sobolev classes

It is proved that homeomorphisms of the Orlicz-Sobolev class Wloc1, φ can be continuously extended to the boundaries of some domains if the function φ defining this class satisfies a Carderón-type condition and the outer dilatation Kf of the mapping f satisfies the divergence condition for integrals of special form. In particular, the result holds for homeomorphisms of the Sobolev classes Wloc1,1 with Kf ∈ Llocq for q > n − 1.

On the zero-dimensionality of the limit of the sequence of generalized quasiconformal mappings

The paper is devoted to the study of the properties of a class of space mappings that is more general than that of bounded distortion mappings (aka quasiregular mappings). It is shown that the locally uniform limit of a sequence of mappings f: D → ℝn of a domain D ⊂ ℝn, n ≥ 2, satisfying one inequality for the p-modulus of families of curves is zero-dimensional. This statement generalizes a well-known theorem on the openness and discreteness of the uniform limit of a sequence of bounded distortion mappings.

On local properties of spatial generalized quasi-isometries

An upper bound for the measure of the image of a ball under mappings of a certain class generalizing the class of branched spatial quasi-isometries is determined. As a corollary, an analog of Schwarz’ classical lemma for these mappings is proved under an additional constraint of integral character. The obtained results have applications to the classes of Sobolev and Orlicz–Sobolev spaces.

On removable singularities of maps with growth bounded by a function

This paper studies questions related to the local behavior of almost everywhere differentiable maps with the N, N−1, ACP, and ACP−1 properties whose quasiconformality characteristic satisfies certain growth conditions. It is shown that, if a map of this type grows in a neighborhood of an isolated boundary point no faster than a function of the radius of a ball, then this point is either a removable singular point or a pole of this map.