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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 1, Pages 166–183 (Mi timm213)  

On Yudin's scheme of finding a lower estimate for the potential energy of a system of charges on a sphere

A. A. Montile

Botanic Garden, Russian Academy of Sciences, Ural Branch

Abstract: We consider Yudin's problem of finding a lower estimate for the minimum of the potential energy of a system of equal charges on the unit sphere $\mathbb S^2$ of Euclidean space $\mathbb R^3$. For this problem, we write a dual problem in the case of an arbitrary number of charges. A solution of the dual problem is given for the cases of 5, 6, 7, 8, and 12 charges. In addition, the primal problem is solved and hypothetically optimal distributions are specified for 7 and 8 charges. It is established that YudinТs method does not allow one to prove the optimality of these distributions.

Keywords: potential energy of a system of charges, Yudin's problem, primal and dual problems, hypothetically

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 265, suppl. 1, S174–S193

Bibliographic databases:

Document Type: Article
UDC: 517.518.86
Received: 01.11.2008

Citation: A. A. Montile, “On Yudin's scheme of finding a lower estimate for the potential energy of a system of charges on a sphere”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 1, 2009, 166–183; Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S174–S193

Citation in format AMSBIB
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\paper On Yudin's scheme of finding a~lower estimate for the potential energy of a~system of charges on a~sphere
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 1
\pages 166--183
\mathnet{http://mi.mathnet.ru/timm213}
\elib{http://elibrary.ru/item.asp?id=11929786}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 265
\issue , suppl. 1
\pages S174--S193
\crossref{https://doi.org/10.1134/S0081543809060145}
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