Loss of derivatives for systems of complex vector fields and sums of squares

TL;DR

This paper explores the phenomenon of hypoellipticity with loss of derivatives in systems of complex vector fields and sums of squares, building on Kohn's discovery.

Contribution

It extends the understanding of hypoellipticity with loss of derivatives to new classes of systems and sums of squares, providing deeper theoretical insights.

Findings

Identifies conditions under which loss of derivatives occurs

Provides examples illustrating hypoellipticity with loss

Enhances theoretical framework for complex vector fields

Abstract

We discuss, both for systems of complex vector fields and for sums of squares, the phenomenon discovered by Kohn of hypoellipticity with loss of derivatives.