Gevrey hypoellipticity for equations with involutive characteristics of higher multiplicity (Q2704754)

This paper deals with Gevrey hypoellipticity for a class of partial differential operators with analytic coefficients. The operators are assumed to have involutive characteristics of multiplicity \(m \geq 4\) and an elliptic subprincipal symbol. The results about \(d\)-microlocal hypoellipticity in the Gevrey spaces \( G_{d} \) are proved by using Fourier integral operators and \( S_{\rho, \delta}^{m} \) arguments. The case \( m =2 \) was studied by \textit{P. R. Popivanov} [Partial differential equations, Banach Cent. Publ. 19, 213-224 (1987; Zbl 0657.35137)] and \textit{R. Lascar} [C. R. Acad. Sci., Paris, Sér. A 284, 485-488 (1977; Zbl 0348.35085)].