Zobrazeno 1 - 10
of 24
pro vyhledávání: '"N. V. Zorii"'
Autor:
N. V. Zorii
Publikováno v:
Ukrainian Mathematical Journal. 58:842-861
We formulate and solve extremal problems of potential theory that are dual to the Gauss variational problem but, unlike the latter, are always solvable. Statements on the compactness of classes of solutions and the continuity of extremals are also es
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::59161c569269d9f2aba1bb11afae38ee
https://doi.org/10.1007/s11253-006-0108-3
https://doi.org/10.1007/s11253-006-0108-3
Autor:
N. V. Zorii
Publikováno v:
Ukrainian Mathematical Journal. 57:70-99
We investigate the well-known Gauss variational problem over classes of Radon measures associated with a system of sets in a locally compact space. Under fairly general assumptions, we obtain necessary and sufficient conditions for its solvability. A
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3c6b82e0101f42df5c484f74f5d4b99c
https://doi.org/10.1007/s11253-005-0172-0
https://doi.org/10.1007/s11253-005-0172-0
Autor:
N. V. Zorii
Publikováno v:
Ukrainian Mathematical Journal. 56:1796-1812
The concept of consistent kernels introduced by Fuglede in 1960 is widely used in extremal problems of the theory of potential on classes of positive measures. In the present paper, we show that this concept is also efficient for the investigation of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8f6d5b914b2462b14c61deb0de574ccb
https://doi.org/10.1007/s11253-005-0152-4
https://doi.org/10.1007/s11253-005-0152-4
Autor:
N. V. Zorii
Publikováno v:
Ukrainian Mathematical Journal. 55:1588-1618
We investigate the problem on the minimum of energy over fairly general (generally speaking, noncompact) classes of real-valued Radon measures associated with a system of sets in a locally compact space in the presence of external fields. The classes
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8c2016f26dfce7145f5a62509e9d506c
https://doi.org/10.1023/b:ukma.0000022070.73078.7b
https://doi.org/10.1023/b:ukma.0000022070.73078.7b
Autor:
N. V. Zorii
Publikováno v:
Ukrainian Mathematical Journal. 55:1423-1444
We investigate the Gauss variational problem over fairly general classes of Radon measures in a locally compact space X. We describe potentials of minimizing measures, establish their characteristic properties, and prove the continuity of extremals.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6be1f82a3336b2f1dbf3e33aa3be2a54
https://doi.org/10.1023/b:ukma.0000018005.67743.86
https://doi.org/10.1023/b:ukma.0000018005.67743.86
Autor:
A. A. Latyshev, N. V. Zorii
Publikováno v:
Ukrainian Mathematical Journal. 54:1471-1491
We pose and solve an extremal problem of logarithmic potential theory that is dual to the main minimum problem in the theory of interior capacities of condensers but, in contrast to the latter, it is solvable even in the case of a nonclosed condenser
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::864cae98e1884d26040ac329a73775fa
https://doi.org/10.1023/a:1023415918753
https://doi.org/10.1023/a:1023415918753
Autor:
N. V. Zorii
Publikováno v:
Ukrainian Mathematical Journal. 53:190-213
The present paper is the first part of a work devoted to the development of the theory of κ-capacities of condensers in a locally compact space X; here, κ: X × X → (−∞, +∞] is a lower-semicontinuous function. Condensers are understood in a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f8752dc60611b965901d4679ff3193d4
https://doi.org/10.1023/a:1010456701920
https://doi.org/10.1023/a:1010456701920
Autor:
N. V. Zorii
Publikováno v:
Ukrainian Mathematical Journal. 48:1889-1903
We introduce and study a one-parameter family of capacity characteristics of condensers in ℝp,p ≥ 3, that contains some known capacities as elements extremal with respect to the parameter. We establish new relations between the capacity character
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c9709b6fb39eb2d78538a213f5ad0bbc
https://doi.org/10.1007/bf02375375
https://doi.org/10.1007/bf02375375
Autor:
N. V. Zorii
Publikováno v:
Ukrainian Mathematical Journal. 48:671-682
We study some generalizations of the well-known problem of minimization of the Riesz energy on condensers. Under fairly general assumptions, we establish necessary and sufficient conditions for the existence of minimal measures.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::744744555b2886dd66a8fe6db0782a85
https://doi.org/10.1007/bf02384234
https://doi.org/10.1007/bf02384234
Autor:
N. V. Zorii
Publikováno v:
Ukrainian Mathematical Journal. 47:1541-1553
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3d3f21daf112750d468ef5b3fc8f70c3
https://doi.org/10.1007/bf01060154
https://doi.org/10.1007/bf01060154