  In this paper we study the Cauchy problem for second order strictly
hyperbolic operators when the coefficients of the principal part are not
Lipschitz continuous, but only "Log-Lipschitz" with respect to all the
variables. This class of equation is invariant under changes of variables and
therefore suitable for a local analysis. In particular, we show local
existence, local uniqueness and finite speed of propagation for the
noncharacteristic Cauchy problem.
