Hypoellipticity and Higher Order Levi Conditions

TL;DR

This paper investigates the smooth hypoellipticity of certain double characteristic operators with symplectic characteristic manifolds, especially when traditional minimal loss conditions are not satisfied, advancing understanding of operator regularity.

Contribution

It introduces new insights into hypoellipticity for operators with complex characteristic structures beyond classical minimal loss scenarios.

Findings

Identifies conditions under which hypoellipticity holds despite violation of minimal loss

Provides a framework for analyzing higher order Levi conditions in complex operators

Extends existing theories to broader classes of differential operators

Abstract

We study the $C^\infty$-hypoellipticity for a class of double characteristic operators with simplectic characteristic manifold, in the case the classical condition of minimal loss of derivatives is violated.