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2020 Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds
David Beltran, Jonathan Hickman, Christopher D. Sogge
Anal. PDE 13(2): 403-433 (2020). DOI: 10.2140/apde.2020.13.403

Abstract

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.

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David Beltran. Jonathan Hickman. Christopher D. Sogge. "Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds." Anal. PDE 13 (2) 403 - 433, 2020. https://doi.org/10.2140/apde.2020.13.403

Information

Received: 15 February 2018; Revised: 27 December 2018; Accepted: 23 February 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07181505
MathSciNet: MR4078231
Digital Object Identifier: 10.2140/apde.2020.13.403

Subjects:
Primary: 35S30
Secondary: 35L05

Keywords: Decoupling inequalities , Fourier integral operators , local smoothing , variable coefficient

Rights: Copyright © 2020 Mathematical Sciences Publishers

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