Перегляд за автором "Ryazanov, V.I."

Сортувати за: Порядок: Результатів:

  • Bojarski, B.V.; Gutlyanskii, V.V.; Ryazanov, V.I. (Український математичний вісник, 2008)
    We study the Beltrami equations ∂f = μ(z)∂f + ν(z)∂f under the assumption that the coefficients μ, ν satisfy the inequality |μ| + |ν| < 1 almost everywhere. Sufficient conditions for the existence of homeomorphic ACL ...
  • Gutlyanskii, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I. (Доповіді НАН України, 2018)
    We study semilinear partial differential equations in the plane, the linear part of which is written in a divergence form. The main result is given as a factorization theorem. This theorem states that every weak solution ...
  • Gutlyanskiĭ, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I. (Доповіді НАН України, 2020)
    The study of the Dirichlet problem with arbitrary measurable boundary data for harmonic functions in the unit disk is due to the famous Luzin dissertation. Later on, the known monograph of Vekua was devoted to ...
  • Ryazanov, V.I.; Volkov, S.V. (Доповіді НАН України, 2020)
    We prove a series of criteria in terms of dilatations for the continuous and homeomorphic extension of the map pings with finite length distortion between domains on Riemann surfaces to the boundary. The criterion for the ...
  • Gutlyanskii, V.Y.; Nesmelova, O.V.; Ryazanov, V.I. (Український математичний вісник, 2016)
    Assume that Ω is a regular domain in the complex plane C and A(z) is symmetric 2 × 2 matrix with measurable entries, det A = 1 and such that 1/K|ξ|² ≤ 〈A(z)ξ, ξ〉 ≤ K|ξ|², ξ ∊ R², 1 ≤ K < ∞. We study the blow-up problem ...
  • Gutlyanskiĭ, V.Ya.; Ryazanov, V.I.; Yefimushkin, A.S. (Доповіді НАН України, 2017)
    We give a short description of our recent results obtained by a new approach to the boundary-value problems, such as the Dirichlet, Hilbert, Neumann, Poincaré and Riemann problems, for the Beltrami equations and for ...
  • Gutlyanskii, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I. (Доповіді НАН України, 2018)
    We study semilinear elliptic equations of the form div(A(z)∇u) = f(u) in Ω⊂ C, where A(z) stands for a symmetric 2×2 matrix function with measurable entries, det A =1, and such that 1/ K |ξ|² ≤ 〈A(z)ξ,ξ〉 ≤ K |ξ|², ξ ∈ R², ...
  • Gutlyanskii, V.Ya.; Ryazanov, V.I.; Yakubov, E.; Yefimushkin, A.S. (Доповіді НАН України, 2019)
    We study the Hilbert boundaryvalue problem for the Beltrami equations in the Jordan domains satisfying the quasihyperbolic boundary condition by Gehring—Martio, generally speaking, without the standard (A)condition by ...
  • Gutlyanskii, V.Y.; Nesmelova, O.V.; Ryazanov, V.I. (Український математичний вісник, 2017)
    Assume that Ω is a domain in the complex plane C and A(z) is symmetric 2× 2 matrix function with measurable entries, det A = 1 and such that 1/K|ξ|²≤ 〈A(z)ξ, ξ〉 ≤ K|ξ|², ξ ∊ R², 1 ≤ K < ∞. In particular, for semi-linear ...
  • Gutlyanskii, V.Y.; Ryazanov, V.I. (Український математичний вісник, 2016)
    The survey is devoted to recent advances in nonclassical solutions of the main boundary value problems such as the well–known Dirichlet, Hilbert, Neumann, Poincare and Riemann problems in the plane. Such solutions are ...
  • Gutlyanskiĭ, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I. (Доповіді НАН України, 2019)
    We study the Dirichlet problem for the semilinear partial differential equations div (A∇u) = f (u) in simply connected domains D of the complex plane C with continuous boundary data. We prove the existence of the weak ...
  • Ryazanov, V.I. (Праці Інституту прикладної математики і механіки НАН України, 2017)
    It is proved that if a harmonic function u on the unit disk D in C has angular limits on a measurable set E of the unit circle, then its conjugate harmonic function v in D also has (finite !) angular limits a.e. on E and ...
  • Gutlyanskii, V.Y.; Ryazanov, V.I.; Yefimushkin, A.S. (Український математичний вісник, 2015)
    Generalized solvability of the classical boundary value problems for analytic and quasiconformal functions in arbitrary Jordan domains with boundary data that are measurable with respect to the logarithmic capacity is ...
  • Gutlyanskii, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I. (Праці Інституту прикладної математики і механіки НАН України, 2017)
    We study the Dirichlet problem for the quasilinear partial differential equations of the form Δu(z) = h(z)·f(u(z)) in the unit disk D ⊂ C with functions h : D → R in the class Lp(D), p > 1, and continuous functions f : R ...
  • Gutlyanskii, V.Ya.; Ryazanov, V.I.; Yakubov, E.; Yefimushkin, A.S. (Доповіді НАН України, 2019)
    We study the Hilbert boundary-value problem for analytic functions in the Jordan domains satisfying the quasi-hyperbolic boundary condition by Gehring—Martio. Assuming that the coefficients of the problem are functions ...
  • Gutlyanskii, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I. (Доповіді НАН України, 2020)
  • 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), ...
  • 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 ...
  • 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.
  • 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.