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Variable coefficient
Wolff-type inequalities and sharp local smoothing estimates
for wave equations on manifolds
David Beltran, Jonathan Hickman and Christopher D. Sogge |
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Vol. 13 (2020), No. 2, 403–433
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Abstract |
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The sharp Wolff-type decoupling estimates of Bourgain and Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian manifolds, away from the endpoint regularity exponent. More generally, local smoothing estimates are established for a natural class of Fourier integral operators; at this level of generality the results are sharp in odd dimensions, both in terms of the regularity exponent and the Lebesgue exponent. |
Keywords
local smoothing, variable coefficient, Fourier integral
operators, decoupling inequalities
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Mathematical Subject Classification 2010
Primary: 35S30
Secondary: 35L05
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Milestones
Received: 15 February 2018
Revised: 27 December 2018
Accepted: 23 February 2019
Published: 19 March 2020
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Authors |
| David Beltran | |
| Basque Center for Applied
Mathematics Bilbao Spain |
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| Jonathan Hickman | |
| Mathematical Institute University of St Andrews St Andrews United Kingdom |
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| Christopher D. Sogge | |
| Department of Mathematics Johns Hopkins University Baltimore, MD United States |
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