August  2007, 1(3): 537-556. doi: 10.3934/ipi.2007.1.537

Stability for solutions of wave equations with $C^{1,1}$ coefficients

1. 

Department of Mathematics and Statistics / RNI, University of Helsinki, P.O. Box 68, 00014 Helsinki

Received  November 2006 Published  July 2007

We consider the stable dependence of solutions to wave equations on metrics in $C^{1,1}$ class. The main result states that solutions depend uniformly continuously on the metric, when the Cauchy data is given in a range of Sobolev spaces. The proof is constructive and uses the wave packet approach to hyperbolic equations.
Citation: Mikko Salo. Stability for solutions of wave equations with $C^{1,1}$ coefficients. Inverse Problems & Imaging, 2007, 1 (3) : 537-556. doi: 10.3934/ipi.2007.1.537
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