We first study the boundary behavior of ring Q-homeomorphisms in terms of Carathéodory's
prime ends and then give criteria to the solvability of the Dirichlet problem for the degenerate …

Abstract Following Bojarski and Vekua, we have studied the Dirichlet problem lim z→ ζ Re
fz= φ ζ as z→ ζ, z∈ D, ζ∈∂ D, with continuous boundary data φ (ζ) in bounded domains D …

We study regular solutions of the nonlinear Cauchy–Riemann–Beltrami equation for the
logarithmic asymptotics in terms of the lower limits and solve an extreme problem for the …

A canonical representation of prime ends is obtained in the case of regular spatial domains,
and the boundary behavior is studied for the so-called lower $ Q $-homeomorphisms, which …

A power estimate of the area of the image of a disk for regular homeomorphisms possessing
the Luzin N-property is obtained in terms of the p-angular dilation for p> 2. The result …

V. Ryazanov, S. Volkov PRIME ENDS IN THE SOBOLEV MAPPING THEORY ON RIEMANN
SURFACES 1. Introduction. The theory of the boundary Page 1 Математичнi Студiї. Т.48 …

We study homeomorphisms and mappings with branching in domains of the Euclidean
space. We establish pointwise HÖlder and Lipschitz properties of mappings whose …

We prove analogs of theorems of Lusin and Gehring in terms of logarithmic capacity. On this
basis, for the nondegenerate Beltrami equations in the quasidisks and, in particular, in …

We investigate the Hilbert boundary-value problem for Beltrami equations∂¯ f ∂ f= μ∂ f
with singularities in generalized quasidisks D whose Jordan boundary∂ D consists of a …

С точки зрения теории конформных отображений было признано не
удовлетворительным рассматривать отдельные точки границы односвязной области …