Gevrey-hypoellipticity for a Class of Parabolic Type Operators

Abstract

This paper studies the micro-local version of the Gevrey-hypoellipticity for a class of parabolic type operator, ∂_t-a(t, x; D_s,) (a(t, x;D_s) (a(t, x; ξ) ∈ C^∞([0, T], S^m_{G^m}(R^n)) (m ≥ 1/s) is a Gevrey-pseudoanaiytic symbol of class s(s > 1)), and we obtain the following main result: Under the condition (I), the operator stated above is micro-local Gevrey-hypoelliptic. In order to prove our main result, the auther have used (α, β) method in this paper.