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Composition operators on Sobolev spaces and weighted moduli inequalities
Vladimir Gol'dshtein, Evgeny Sevost'yanov, Alexander Ukhlov
In this paper we study connections between composition operators on Sobolev spaces and mappings defined by -moduli inequalities (-capacity inequalities). We prove that weight…
On compactness of one class of solutions of the Dirichlet problem
Oleksandr Dovhopiatyi, Evgeny Sevost'yanov
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 normalizat…
On the inverse -inequality for one class of mappings
Oleksandr Dovhopiatyi, Evgeny Sevost'yanov
We study mappings differentiable almost everywhere, possessing the -Luzin property, the -property on the spheres with respect to the -dimensional Hausdorff mea…
On the inverse Poletskii inequality in metric spaces and prime ends
Evgeny Sevost'yanov
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, i…
Mappings with the inverse Poletsky inequality are discrete on the boundary
Evgeny Sevost'yanov
It is established a continuous boundary extension of some class of mappings. Under some additional conditions, we have established that this extension is light in the closure of th…