Improved local smoothing estimate for the wave equation in higher dimensions
Analysis of PDEs
2023-04-11 v2 Classical Analysis and ODEs
Abstract
In this paper, we establish the sharp -broad estimate for a class of phase functions satisfying the homogeneous convex conditions. As an application, we obtain improved local smoothing estimates for the half-wave operator in dimensions . As a byproduct, we also generalize the restriction estimates of Ou--Wang to a broader class of phase functions.
Cite
@article{arxiv.2108.06870,
title = {Improved local smoothing estimate for the wave equation in higher dimensions},
author = {Chuanwei Gao and Bochen Liu and Changxing Miao and Yakun Xi},
journal= {arXiv preprint arXiv:2108.06870},
year = {2023}
}
Comments
32 pages, 3 figures, Referees' suggestions incorporated. To appear in J. Func. Anal