#### Vol. 7, No. 5, 2014

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
Propagation of singularities for rough metrics

### Hart F. Smith

Vol. 7 (2014), No. 5, 1137–1178
##### 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 ${L}_{t}^{1}{L}_{x}^{\infty }$, and that $u$ is a solution to the homogeneous equation of global Sobolev regularity ${s}_{0}=0$ or 1. It is then proven that the ${H}^{{s}_{0}+1}$ wavefront set of $u$ is a union of maximally extended null bicharacteristic curves.

##### Keywords
wavefront set, wave equation, propagation of singularities
##### Mathematical Subject Classification 2010
Primary: 35A21, 35L10
##### Milestones
Received: 18 February 2014
Accepted: 11 April 2014
Published: 27 September 2014
##### Authors
 Hart F. Smith Department of Mathematics University of Washington Box 354350 Seattle, WA 98195-4350 United States