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Global parametrices and dispersive estimates for variable coefficient wave equations

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Abstract

In this article we consider variable coefficient time dependent wave equations in \({\mathbb {R} \times \mathbb {R}^n}\) . Using phase space methods we construct outgoing parametrices and prove Strichartz type estimates globally in time. This is done in the context of C 2 metrics which satisfy a weak asymptotic flatness condition at infinity.

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599-3250, USA

    Jason Metcalfe

  2. Department of Mathematics, University of California, Berkeley, CA, 94720-3840, USA

    Daniel Tataru

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  1. Jason Metcalfe
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  2. Daniel Tataru
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Correspondence to Jason Metcalfe.

Additional information

The work of the first author was supported in part by an NSF postdoctoral fellowship and NSF grant DMS0800678, and that of the second author by NSF grants DMS0354539 and DMS0301122.

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Metcalfe, J., Tataru, D. Global parametrices and dispersive estimates for variable coefficient wave equations. Math. Ann. 353, 1183–1237 (2012). https://doi.org/10.1007/s00208-011-0714-8

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  • DOI: https://doi.org/10.1007/s00208-011-0714-8

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