Registration Number
0221U102786,
0116U002034
, R & D reports
Title
Geometric, topological and approximate problems of the function theory with applications to problems of the mathematical physics in nonhomogeneous media
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Head
Ryazanov Volodymyr I., Доктор фізико-математичних наук
Registration Date
10-02-2021
Organization
Institute of Applied Mathematics and Mechanics National Academy of Science of Ukraine
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Theorems on existence, regularity and representation of nonclassical solutions of boundary value problems of Riemann, Hilbert, Dirichlet, Neumann and Poincaré for equations of mathematical physics in anisotropic and inhomogeneous media with continuous and with arbitrary measurable boundary data were established. Conditions for the coefficient of degenerate Beltrami equations were found, under which solutions of these equations were Hölder continuous at boundary points. Inequalities of Hölder and Lipschitz type were established for spatial mappings, the characteristics of which satisfy conditions of Dini type. It was proved convergence a.e. of singular Hilbert-Stieltjes integral and the existence of the angular limits a.e. of the Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes integrals for arbitrary bounded integrants that differentiate a.e., in particular, for arbitrary integrants of bounded variation. New estimates of the moduli of smoothness and deviations of the best approximations of functions by splines, trigonometric and algebraic polynomials are obtained. Asymptotic structure of pre-tangent spaces to metric spaces at infinity was studied and, in particular, a geometric description of unbounded metric spaces with finite clusters of pre-tangent spaces was given. Conditions for metric spaces to be minimal universal in a given class of metric spaces were obtained. Criteria for the isomorphism of ordinal spaces were found and the problem on the imbedding of the ordinal spaces in a real line and in Euclidean spaces of higher dimension was studied. An analogue of the Sokhotsky–Kasorati–Weierstrass theorem for mappings of metric spaces was obtained. The boundary and local behavior of modern classes of mappings on manifolds were studied. Integral criteria of Lavrentiev-Zorich-Lehto, Orlicz, Calderon-Zygmund, John-Nierenberg types and others were established for extending to the boundary mappings on Riemann surfaces.
Product Description
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Yefimushkin Artem S
Afanas’eva Elena S
Bilet Victoria V
Gutlyansky Volodymyr Ya
Dovgoshey Oleksiy A.
Kolomoitsev Yurii S
Lomako Tetiana V
Nesmelova Olga V
Petrov Yevgen O
Sevost'yanov Evgenii O
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2021-02-10
