Global conservation law for an even order elliptic system with antisymmetric potential

TL;DR

This paper extends local conservation laws for even order elliptic systems with antisymmetric potentials to a global setting, refining previous results for fourth order and general systems.

Contribution

It provides a global conservation law for even order elliptic systems with antisymmetric potentials, building on and refining prior local results.

Findings

Established a global conservation law for the systems.

Extended previous local results to a global context.

Applicable to a broad class of even order elliptic systems.

Abstract

In this note, we refine the local conservation law obtained by Lamm-Rivi\`ere for fourth order systems and de Longueville-Gastel for general even order systems to a global conservation law.