Geometric Results for a Class of Hyperbolic Operators with Double Characteristics ,II.

✍ Scribed by E. Bernardi; A. Bove; C. Parenti

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 658 KB
• Volume: 116
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1993.1104

✦ Synopsis

Let (p) be the principal symbol of a hyperbolic (pseudo) differential operator of order (m) admitting at most double characteristic roots. Suppose that at each point (\rho) of the double characteristic manifold (\Sigma) of (p) the Hamiltonian matrix of (p, F_{p}), has a Jordan block of dimension 4 . We prove a necessary and sufficient condition on (p) in order that its bicharacteristic curves have limit points belonging to (\Sigma). It is shown that if no bicharacteristic curve of (p) has a limit point belonging to (\Sigma) then the Cauchy problem for (p) is well-posed, provided the usual Levi conditions on the lower order terms are satisfied. 1993 Academic Press, Inc.