Cauchy Problem for Differential Operators with Double Characteristics

Features thorough discussions on well/ill-posedness of the Cauchy problem for dierential operators with double characteristics of non-eectively hyperbolic type

Takes a unied approach combining geometrical and microlocal tools

Adopts the viewpoint that the Hamilton map and the geometry of bicharacteristics characterizes the well/ill-posedness of the Cauchy problem

Inhalt

1. Introduction.- 2 Non-effectively hyperbolic characteristics.- 3 Geometry of bicharacteristics.- 4 Microlocal energy estimates and well-posedness.- 5 Cauchy problemno tangent bicharacteristics. - 6 Tangent bicharacteristics and ill-posedness.- 7 Cauchy problem in the Gevrey classes.- 8 Ill-posed Cauchy problem, revisited.- References.