Multi-Parameter Div-Curl Lemmas

TL;DR

This paper explores multi-parameter analogs of the Div-Curl Lemma in harmonic analysis and PDEs, introducing two variants and extending the results to differential forms.

Contribution

It introduces two new multi-parameter Div-Curl lemmas and extends the theory to differential forms, broadening the classical understanding.

Findings

Two multi-parameter Div-Curl lemmas are established.

Extensions of these lemmas to differential forms are provided.

The work advances the theoretical framework in harmonic analysis and PDEs.

Abstract

We study the possible analogous of the Div-Curl Lemma in classical harmonic analysis and partial differential equations, but from the point of view of the multi-parameter setting. In this context we see two possible Div-Curl lemmas that arise. Extensions to differential forms are also given.