Propagation of Singularities for Rough Metrics

We use a wave packet transform and weighted norm estimates in phase space to establish propagation of singularities for solutions to timedependent scalar hyperbolic equations that have coefficients of limited regularity. It is assumed that the second order derivatives of the principal coefficients belong to LtL ∞ x , and that u is a solution to the homogeneous equation, of global Sobolev regularity s0 = 0 or 1. It is then proven that the Hs0+1 wavefront set of u is a union of maximally extended null bicharacteristic curves.