On hypoelliptic differential operators of constant strength

M. Shafii-Mousavi and Zbigniew Zielezny

Vol. 82 (1979), No. 1, 249–256

DOI: 10.2140/pjm.1979.82.249

Abstract

A hypoelliptic differential operator P(D) with constant coefficients has the following property: For every u ∈𝒟′(Ω), if P(D)u is in a Gevrey class in Ω then so is u (though the two Gevrey classes are not necessarily the same).

In this paper we prove that hypoelliptic differential operators with variable coefficients have locally the same property, if they are of constant strength and their coefficients are in a Gevrey class.

Mathematical Subject Classification

Primary: 35H05, 35H05

Milestones

Received: 31 May 1978

Published: 1 May 1979