TY - JOUR
T1 - Gevrey-hypoellipticity for a Class of Parabolic Type Operators
AU - Chen Hua
JO - Journal of Partial Differential Equations
VL - 2
SP - 63
EP - 76
PY - 1990
DA - 1990/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5799.html
KW - Gevrey-hypoellipticity
KW -  wave front set in Gevrey-class
KW -  (&#945
KW - &#946) method
AB -  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.