Higher order analogues of exterior derivative

TL;DR

This paper introduces new linear differential operators of odd order that are invariant under Euclidean isometries and satisfy specific duality and inequality estimates, expanding the understanding of differential operator properties.

Contribution

It provides novel examples of higher-order invariant differential operators with established duality and div/curl inequalities, advancing the theory of such operators.

Findings

New invariant differential operators of order 2m+1

Operators satisfy L^1-duality estimates

Operators meet div/curl inequalities

Abstract

We give new examples of linear differential operators of order $k=2m+1$ (any given odd integer) that are invariant under the isometries of $\mathbb R^n$ and satisfy so-called $L^1$-duality estimates and div/curl inequalities.