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

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  • 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.
    Mathematics Subject Classification: Primary: 35L05, 35A17, 35B35, 35R30.

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