Energy of solenoidal vector fields on spherical domains

TL;DR

This paper extends a theorem about solenoidal unit vector fields with minimal energy to spherical domains, providing a boundary version applicable to odd-dimensional Euclidean spheres.

Contribution

It introduces a boundary version of the minimal energy theorem for solenoidal vector fields on spherical domains in odd dimensions.

Findings

Established a boundary version of the minimal energy theorem

Applied the theorem to odd-dimensional Euclidean spheres

Enhanced understanding of energy minimization in vector fields

Abstract

We present a boundary version of a theorem about solenoidal unit vector fields with minimum energy on a spherical domain of an odd dimensional Euclidean sphere.