Formally Integrable Structures II. Division Problem

TL;DR

This paper addresses a division problem for overdetermined systems in PDEs, providing a divisibility criterion and extending coherence theorems to elliptic systems, advancing the theoretical understanding of PDE structures.

Contribution

It introduces a new divisibility criterion for overdetermined PDE systems and extends Nadel's coherence theorem to elliptic systems, broadening the scope of existing PDE theory.

Findings

Established an effective divisibility criterion.

Proved a coherence theorem for elliptic systems.

Extended Nadel's coherence theorem to new PDE classes.

Abstract

We formulate a division problem for a class of overdetermined systems introduced by L. H{\"o}rmander, and establish an effective divisibility criterion. In addition, we prove a coherence theorem which extends Nadel's coherence theorem from complex structures to elliptic systems of partial differential equations.