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# Перегляд за автором "Nesmelova, O.V."

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• (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 ...
• (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 ...
• (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 ...
• (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 ...
• (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 ...
• (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, ...
• (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 ...
• (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 ...
• (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 ...
• (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 ...
• (Доповіді НАН України, 2020)
• (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), ...
• (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 ...
• (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. ...
• (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 ...
• (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 ...