Optimal discrete Neumann energy in a ball and a circular ring

TL;DR

This paper provides exact estimates for the discrete Neumann energy in specific geometric domains, using dissymmetrization and asymptotic analysis of potential functions.

Contribution

It introduces new precise estimates for discrete Neumann energy in a ball and circular ring, advancing understanding of potential theory in these shapes.

Findings

Exact estimates for Neumann energy in a ball.

Exact estimates for Neumann energy in a circular ring.

Use of dissymmetrization and asymptotic analysis techniques.

Abstract

In this paper, we prove some exact estimates for the discrete Neumann energy of a ball and a circular ring 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.