Перегляд за автором "Nesmelova, O.V."

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 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 ...
  • 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 ...
  • 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 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 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 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 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 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), ...
  • 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 ...
  • 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 Dirichlet problem for the Poisson type equations in the plane 
    Gutlyanskiĭ, V.Ya.; Nesmelova, O.V. (Доповіді НАН України, 2020)
    We present a new approach to the study of 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 A(z), whereas its ...
  • 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 ...