Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds
Analysis of PDEs
2020-03-25 v2 Classical Analysis and ODEs
Abstract
The sharp Wolff-type decoupling estimates of Bourgain--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.
Cite
@article{arxiv.1801.06910,
title = {Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds},
author = {David Beltran and Jonathan Hickman and Christopher D. Sogge},
journal= {arXiv preprint arXiv:1801.06910},
year = {2020}
}
Comments
27 pages, 3 figures. Update incorporates referee suggestions. Minor correction to the proof of Lemma 2.6. To appear in APDE