Translator Disclaimer
2019 Dispersive estimates for the wave equation on Riemannian manifolds of bounded curvature
Yuanlong Chen, Hart F. Smith
Pure Appl. Anal. 1(1): 101-148 (2019). DOI: 10.2140/paa.2019.1.101

Abstract

We prove space-time dispersive estimates for solutions to the wave equation on compact Riemannian manifolds with bounded curvature tensor, where we assume that the metric tensor is of W 1 , p regularity for some p > d , which ensures that the curvature tensor is well-defined in the weak sense. The estimates are established for the same range of Lebesgue and Sobolev exponents that hold in the case of smooth metrics. Our results are for bounded time intervals, so by finite propagation velocity they hold also on noncompact manifolds under appropriate uniform geometry conditions.

Citation

Download Citation

Yuanlong Chen. Hart F. Smith. "Dispersive estimates for the wave equation on Riemannian manifolds of bounded curvature." Pure Appl. Anal. 1 (1) 101 - 148, 2019. https://doi.org/10.2140/paa.2019.1.101

Information

Received: 8 August 2018; Revised: 12 September 2018; Accepted: 22 October 2018; Published: 2019
First available in Project Euclid: 4 February 2019

zbMATH: 07027486
MathSciNet: MR3900030
Digital Object Identifier: 10.2140/paa.2019.1.101

Subjects:
Primary: 58J45
Secondary: 35L15

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
48 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.1 • No. 1 • 2019
MSP
Back to Top