Geodesic
Optimal discrete Neumann energy in a ball and an annulus
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 109-119

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In this paper, we prove some exact estimates for the discrete Neumann energy of a ball and an annulus in Euclidean space for points located on circles. The proofs are based on dissymmetrization and analysis of the asymptotic behavior of the Dirichlet integral of the potential function.
Keywords: discrete energy, Green function, Neumann function, dissymmetrization. 
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     author = {E. G. Prilepkina and A. S. Afanaseva-Grigoreva},
     title = {Optimal discrete {Neumann} energy in a ball and an annulus},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a29/}
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E. G. Prilepkina; A. S. Afanaseva-Grigoreva. Optimal discrete Neumann energy in a ball and an annulus. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 109-119. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a29/