Propagation of singularities in the Cauchy problem for a class of degenerate hyperbolic operators

We consider second order degenerate hyperbolic Cauchy problems, the degeneracy coming either from low regularity (less than Lipschitz continuity) of the coefficients with respect to time, or from weak hyperbolicity. In the weakly hyperbolic case, we assume an intermediate condition between effective hyperbolicity and the Levi condition. We construct the fundamental solution and study the propagation of singularities using an unified approach to these different kinds of degeneracy.