On Div-Curl for Higher Order

TL;DR

This paper introduces new complexes of differential operators of arbitrary order that satisfy div-curl and L^1-duality estimates, expanding the understanding of higher-order differential operator complexes.

Contribution

It provides novel examples of higher-order differential complexes that fulfill div-curl and duality estimates, extending classical results to arbitrary order.

Findings

New complexes of differential operators of order k are constructed.

These complexes satisfy div-curl and L^1-duality estimates.

The results generalize classical div-curl theory to higher orders.

Abstract

We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.