Massimo Cicognani

Well-Posedness of the Cauchy Problem for Some Degenerate Hyperbolic Operators

We use an uniform approach to different kinds of degenerate hyperbolic Cauchy problems to prove well-posedness in C∞ and in Gevrey classes. We prove in particular that we can treat by the same method a weakly hyperbolic problem, satisfying an intermediate condition between effective hyperbolicity and the Levi condition, and a strictly hyperbolic problem with non-regular coefficients with respect to the time variable.

The Fundamental Solution for a Second Order Weakly Hyperbolic Cauchy problem

We construct the fundamental solution for a weakly hyperbolic operator satisfying an intermediate condition between effective hyperbolicity and the Levi condition. By the fundamental solution, we obtain the well-posedness in C ⋅ of the Cauchy problem.