Registration Number
0220U104414,
0119U102369
, R & D reports
Title
Geometric and analytical methods for studying extremal problems and partial differential equations
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Head
Denega Iryna V., Кандидат фізико-математичних наук
Registration Date
17-12-2020
Organization
The Institute of Mathematics of NASU
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In the work effective upper estimates for maximums of products of the inner radii of nonoverlapping domains on the radial systems of points of the complex plane for all possible values of some parameter are obtained and conditions under which in the proved results the configuration of domains and points is not important are established. The corresponding results are obtained for the case when the points are placed on a unit circle or an arbitrary line and for the case when the domains are symmetric with respect to the unit circle. On the basis of the obtained estimates of the functionals the enhanced results concerning the exact solutions of an open extremal problems on mutually nonoverlapping domains of the complex plane in the case of free poles of the corresponding quadratic differentials are established. The lower ball volume estimates for homeomorphic mappings relative to a non-conformal module in multidimensional Euclidean space are obtained. Extremal problems on minimizing the functional of the volume of the sphere image in a multidimensional Euclidean space are solved. The class of quaternionic functions analytic by Hausdorff is determined, the relation between the known classes of quaternionic differential functions and the functions analytic by Hausdorff is established, the relation between the known definitions of derivatives and the derivative of Hausdorff is established.
Product Description
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Klishchuk Bogdan A.
Shpakivskyi Vitalii S.
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2020-12-17
