Vol. 7, No. 5, 2014

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
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 Lt1Lx, 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.

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