Vol. 82, No. 1, 1979

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On hypoelliptic differential operators of constant strength

M. Shafii-Mousavi and Zbigniew Zielezny

Vol. 82 (1979), No. 1, 249–256

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
Received: 31 May 1978
Published: 1 May 1979
M. Shafii-Mousavi
Zbigniew Zielezny