Перегляд за автором "Ryazanov, V.I."

Сортувати за: Порядок: Результатів:

  • On the quasilinear Poisson equations in the complex plane 
    Gutlyanskii, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I. (Доповіді НАН України, 2020)
  • On the regularity of solutions of quasilinear Poisson equations 
    Gutlyanskiĭ, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I. (Доповіді НАН України, 2018)
    We study the Dirichlet problem for quasilinear partial differential equations of the form Δu(z) = h(z)f(u(z)) in the unit disk D ⊂ C with continuous boundary data. Here, the function h : D→R belongs to the class L^p(D), ...
  • On the theory of the Beltrami equation 
    Ryazanov, V.I.; Srebro, U.; Yakubov, E. (Український математичний журнал, 2006)
    We study ring homeomorphisms and, on this basis, obtain a series of theorems on existence of the so-called ring solutions for degenerate Beltrami equations. A general statement on the existence of solutions for the ...
  • Poincaré problem with measurable data for semilinear Poisson equation in the plane 
    Gutlyanskiĭ, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I.; Yefimushkin, A.S. (Доповіді НАН України, 2022)
    We study the Poincaré boundary-value problem with measurable in terms of the logarithmic capacity boundary data for semilinear Poisson equations defined either in the unit disk or in Jordan domains with quasihyperbolic ...
  • Prime ends in the mapping theory on the Riemann surfaces 
    Ryazanov, V.I.; Volkov, S.V. (Український математичний вісник, 2017)
    It is proved criteria for continuous and homeomorphic extension to the boundary of mappings with finite distortion between domains on the Riemann surfaces by prime ends of Caratheodory.
  • Prime ends on the Riemann surfaces 
    Ryazanov, V.I.; Volkov, S.V. (Доповіді НАН України, 2017)
    We prove criteria for the homeomorphic extension of mappings with finite distortion between the domains on Riemann surfaces to the boundary by prime Carathéodory ends.
  • Semilinear equations in a plane and quasiconformal mappings 
    Gutlyanskiĭ, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I. (Доповіді НАН України, 2017)
    We consider generalizations of the Bieberbach equation with nonlinear right parts, which makes it possible to study many problems of mathematical physics in inhomogeneous and anisotropic media with smooth characteristics. ...
  • The Beltrami equations and lower Q-homeomorphisms 
    Kovtonyuk, D.A.; Petkov, I.V.; Ryazanov, V.I. (Труды Института прикладной математики и механики, 2010)
    In this article it is shown that each homeomorphic W1,1loc solution to the Beltrami equation ∂f = μ∂f is the so-called lower Q-homeomorphism with Q(z) = Kμ(z) where Kμ(z) is dilatation quotient of this equation. It is ...
  • The Beltrami equations and prime ends 
    Gutlyanskii, V.Y.; Ryazanov, V.I.; Yakubov, E. (Український математичний вісник, 2015)
    We first study the boundary behavior of ring Q-homeomorphisms in terms of Carath´eodory’s prime ends and then give criteria to the solvability of the Dirichlet problem for the degenerate Beltrami equation ∂f = μ∂f in ...
  • The Cauchy-Stieltjes integrals in the theory of analytic functions 
    Ryazanov, V.I. (Український математичний вісник, 2017)
    We study various Stieltjes integrals as Poisson–Stieltjes, conjugate Poisson–Stieltjes, Schwartz–Stieltjes and Cauchy–Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the ...
  • The Dirichlet problem for a Beltrami equation of the second type 
    Bojarski, B.V.; Gutlyanskiĭ, V.Ya.; Ryazanov, V.I. (Доповіді НАН України, 2013)
  • To the theory of semi-linear equations in the plane 
    Gutlyanskii, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I. (Український математичний вісник, 2019)
    In two dimensions, we present a new approach to the study of the semilinear equations of the form div[A(z)∇u] = f(u), the diffusion term of which is the divergence uniform elliptic operator with measurable matrix functions ...
  • Toward the theory of the Dirichlet problem for the Beltrami equations 
    Gutlyanskii, V.Ya.; Ryazanov, V.I.; Yakubov, E. (Доповіді НАН України, 2015)
    The Dirichlet problem for the degenerate Beltrami equations in arbitrary finitely connected domains is studied. In terms of the tangent dilatations, a series of criteria for the existence of regular solutions in arbitrary ...
  • Uniqueness of approximate solutions of the Beltrami equations 
    Kolomoitsev, Yu.S.; Ryazanov, V.I. (Труды Института прикладной математики и механики, 2009)
    We introduce a notion of an approximate solution to the Beltrami equations, obtain some properties of such solutions and show that the approximate solution is unique up to pre-composition with a conformal mapping.