Перегляд за автором "Ryazanov, V.I."

Сортувати за: Порядок: Результатів:

  • Dirichlet problem with measurable data for semilinear equations in the plane 
    Gutlyanskiĭ, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I.; Yefimushkin, A.S. (Доповіді НАН України, 2022)
    The study of the Dirichlet problem with arbitrary measurable data for harmonic functions in the unit disk D goes to the known dissertation of Luzin. His result was formulated in terms of angular limits (along nontangent ...
  • General Beltrami equations and BMO 
    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 ...
  • General elliptic boundary-value problems in Hörmander—Roitberg spaces 
    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 ...
  • Hilbert problem with measurable data for semilinear equations of the Vekua type 
    Gutlyanskiĭ, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I.; Yefimushkin, A.S. (Доповіді НАН України, 2022)
    We prove the existence of solutions for the Hilbert boundary-value problem with arbitrary measurable data for the nonlinear equations of the Vekua’s type ∂Z̅̄f(z) = h(z)q(f(z)). The found solutions differ from the classical ...
  • Hydrodynamic normalization conditions in the theory of degenerate Beltrami equations 
    Gutlyanskiĭ, V.Ya.; Ryazanov, V.I.; Sevost’yanov, E.A.; Yakubov, E. (Доповіді НАН України, 2023)
    Досліджено існування нормалізованих гомеоморфних розв’язків для виродженого рівняння Бельтрамі у всій комплексній площині з припущенням, що його вимірний коефіцієнт має компактний носій, а виродження рівняння контролюється ...
  • Logarithmic capacity and Riemann and Hilbert problems for generalized analytic functions 
    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 ...
  • Mappings with finite length distortion and Riemann surfaces 
    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 ...
  • On a model semilinear elliptic equation in the plane 
    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 ...
  • On a new approach to the study of plane boundary-value problems 
    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 ...
  • On blow-up solutions and dead zones in semilinear equations 
    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, ...
  • On boundary-value problems for generalized analytic and harmonic functions 
    Gutlyanskiĭ, V.Ya.; Nesmelova, O.V.; Ryazanov, V.I.; Yefimushkin, A.S. (Доповіді НАН України, 2020)
    The present paper is a natural continuation of our last articles on the Riemann, Hilbert, Dirichlet, Poincaré, and, in particular, Neumann boundary-value problems for quasiconformal, analytic, harmonic functions and the ...
  • On boundary value problems in domains without (A)-condition 
    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 ...
  • On quasiconformal maps and semi-linear equations in the plane 
    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 ...
  • On recent advances in boundary value problems in the plane 
    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 ...
  • On semilinear equations in the complex plane 
    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 ...
  • On the boundary behavior of conjugate harmonic functions 
    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 ...
  • On the boundary-value problems for quasiconformal functions in the plane 
    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 ...
  • On the Dirichlet problem for degenerate Beltrami equations 
    Gutlyanskiĭ, V.Ya.; Ryazanov, V.I.; Sevost’yanov, E.A.; Yakubov, E. (Доповіді НАН України, 2023)
    Вивчається задача Діріхле для виродженого рівняння Бельтрамі з неперервними межовими даними у довільній однозв’язній області комплексної площини. Встановлені критерії існування регулярних дискретних відкритих розв’язків ...
  • On the Dirichlet problem for quasilinear Poisson equations 
    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 ...
  • On the Hilbert problem for analytic functions in quasihyperbolic domains 
    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 ...