Gevrey-hypoellipticity for a Class of Parabolic Type Operators (Journal of Partial Differential Equations, 1990)
This paper studies the micro-local version of the Gevrey-hypoellipticity for a class of parabolic type operator, &#8706_t-a(t, x; D_s,) (a(t, x;D_s) (a(t, x; &#958) &#8712 C^&#8734([0, T], S^m_{G^m}(R^n)) (m &#8805 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 (&#945, &#946) method in this paper.
Keywords: Gevrey-hypoellipticity; wave front set in Gevrey-class; (α&#946) method