E. G. Prilepkina, A. S. Afanaseva-Grigoreva, “Optimal discrete Neumann energy in a ball and an annulus”, Sib. Èlektron. Mat. Izv., 2022, Volume 19, Issue 1,Pages <nobr>109

This article is cited in 1 paper

Real, complex and functional analysis

Optimal discrete Neumann energy in a ball and an annulus

E. G. Prilepkina^ab, A. S. Afanaseva-Grigoreva^a

^a Far Eastern Federal University, 10, Ajax Bay, Russky Island, Vladivostok, 690922, Russia
^b Institute of Applied Mathematics, FEBRAS, 7, Radio str., Vladivostok, 690041, Russia

Abstract: 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.

UDC: 517.956.224

MSC: 31A15

Received September 6, 2021, published February 3, 2022

Language: English

DOI: 10.33048/semi.2022.19.010