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On Beltrami equations with the inverse conditions and hydrodynamic normalization
Evgeny Sevost'yanov, Oleksandr Dovhopiatyi
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 th…
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 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…
Isolated singularities of mappings with the inverse Poletski inequality
Evgeny Sevost'yanov
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 c…
On the local and boundary behavior of mappings on factor-spaces
Evgeny Sevost'yanov
In this article, we study mappings acting between domains of two factor spaces by certain groups of Möbius automorphisms of the unit ball that act discontinuously and do not have f…
On the existence of a solution of the Beltrami equation with degeneration
Evgeny Sevost'yanov
We have found one of the possible conditions under which the Beltrami equation with degeneration of ellipticity has a continuous solution of the Sobolev class. With some additional…