Abstract
We use a wave packet transform and weighted norm estimates in phase space to establish propagation of singularities for solutions to time-dependent scalar hyperbolic equations that have coefficients of limited regularity. It is assumed that the second order derivatives of the principal coefficients belong to , and that is a solution to the homogeneous equation of global Sobolev regularity or 1. It is then proven that the wavefront set of is a union of maximally extended null bicharacteristic curves.
Citation
Hart Smith. "Propagation of singularities for rough metrics." Anal. PDE 7 (5) 1137 - 1178, 2014. https://doi.org/10.2140/apde.2014.7.1137
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