We study the microlocal regularity of the analytic/Gevrey vectors for the following class of second order partial differential equations \begin{ align*} P(x,D) = \sum_{ \ell,j=1}^{ n} a_{ \ell,j}(x) D_{ \ell} D_{ j} + \sum_{ \ell=1}^{ n} i b_{ \ell}(x) D_{ \ell} +c(x), \end{ align*} where $a_{ \ell,j}(x) = a_{ j,\ell}(x)$, $b_{ \ell}(x)$, $\ell,j \in \lbrace 1,\dots,\, n\rbrace$, are real valued real Gevrey functions of order $s$ and $c(x)$ is a Gevrey function of order $s$, $s \geq 1$, on $\Omega$ open neighborhood of the origin in $\mathbb{ R}^{ n}$. Thus providing a microlocal version of a result due to M. Derridj in "Gevrey regularity of Gevrey vectors of second order partial differential operators with non negative characteristic form", Complex Anal. Synerg. $\mathbf{ 6}$, 10 (2020), https://doi.org/10.1007/s40627-020-00047-8.

Categories: math.AP

On the Microlocal Regularity of the Gevrey Vectors for second order partial differential operators with non negative characteristic form of first kind