Propagation of regularity for a class of systems of real vector fields on torus

TL;DR

This paper characterizes the regularity and solvability properties of systems of real vector fields on the torus, establishing a key theorem on the propagation of regularity for solutions.

Contribution

It introduces a new theorem on the propagation of regularity for systems of real vector fields on the torus, linking hypoellipticity and solvability.

Findings

Characterization of global hypoellipticity and solvability

Theorem on propagation of regularity for solutions

Analysis of sum of squares associated with the system

Abstract

We characterize the global hypoellipticity, almost hypoellipticity and solvability for a class of systems of real vector fields on the (n + 1)-dimensional torus as well as the same properties about the sum of squares associated to the system. The key result is a theorem about propagation of regularity for solutions of the system.