Geometric transition for a class of hyperbolic operators with double characteristics (Q1898248)

The purpose of this work is the study of the Cauchy problem in \(C^\infty\) category for hyperbolic operators with double characteristics under some geometrical perspectives. It is assumed that the set of double characteristic points is a \(C^\infty\) manifold and can be written as the reunion of non-empty subsets, i.e. the set of effectively hyperbolic double points and its complementary. It is proved that the Cauchy problem for degenerate effectively hyperbolic operators is \(C^\infty\) well posed under a certain Levi condition on its subprincipal part, which \textit{R. Melrose} formulated in [Seminar on nonlinear PDEs, Vol. 2, Springer, 185-201 (1984; Zbl 0599.35095)].