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Resolvent estimates
for spacetimes bounded by Killing horizons
Oran Gannot |
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Vol. 12 (2019), No. 2, 537–560
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DOI: 10.2140/apde.2019.12.537
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Abstract |
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We show that the resolvent grows at most exponentially with frequency for the wave equation on a class of stationary spacetimes which are bounded by nondegenerate Killing horizons, without any assumptions on the trapped set. Correspondingly, there exists an exponentially small resonance-free region, and solutions of the Cauchy problem exhibit logarithmic energy decay. |
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Keywords
logarithmic decay, resolvent bounds, Killing horizons,
Carleman estimates
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Mathematical Subject Classification 2010
Primary: 35L05, 35P25, 35R01, 83C57
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Milestones
Received: 20 February 2018
Revised: 27 April 2018
Accepted: 30 May 2018
Published: 14 August 2018
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Authors |
| Oran Gannot | |
| Department of Mathematics Northwestern University Evanston, IL United States |
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