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This article is cited in 5 scientific papers (total in 5 papers)
Green energy and extremal decompositions
V. N. Dubininab a Far Eastern Federal University, 8 Sukhanov str., Vladivostok, 690090, Russia
b Institute of Applied Mathematics, Far Eastern Branch of RAS,
7 Radio str., Vladivostok, 690041, Russia
Abstract:
We give two precise estimates for the Green energy of a discrete charge, concentrated in an even number of points on the circle, with respect to the concentric ring.
The lower estimate for the Green energy is attained for the points with a nonstandard symmetry.
The well-known Pólya-Schur inequality for the logarithmic energy is a special case of this estimate.
The proof is based on the application of dissymmetrization and an asymptotic formula for the conformal capacity of a generalized condenser in the case when some of its plates contract to given points.
The upper bound is established for a charge that takes values of opposite signs.
Its proof reduces to solving a problem on the so-called extremal decomposition of a circular ring with free poles on a circle.
Keywords:
Green energy, discrete charge, dissymmetrization, extremal decompositions.
Received: 18.07.2019 Revised: 30.10.2019 Accepted: 14.10.2019
Citation:
V. N. Dubinin, “Green energy and extremal decompositions”, Probl. Anal. Issues Anal., 8(26):3 (2019), 38–44
Linking options:
https://www.mathnet.ru/eng/pa270 https://www.mathnet.ru/eng/pa/v26/i3/p38
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