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STRICHARTZ ESTIMATES FOR THE WAVE EQUATION INSIDE CYLINDRICAL CONVEX DOMAINS

Part of: Harmonic analysis in several variables Hyperbolic equations and systems

Published online by Cambridge University Press:  08 August 2022

LEN MEAS Open the ORCID record for LEN MEAS [Opens in a new window]
LEN MEAS*
Affiliation:
Department of Mathematics, Royal University of Phnom Penh, Phnom Penh, Cambodia
*
e-mail: meas.len@rupp.edu.kh
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Abstract

We establish local-in-time Strichartz estimates for solutions of the model case Dirichlet wave equation inside cylindrical convex domains $\Omega \subset \mathbb {R}^ 3$ with smooth boundary $\partial \Omega \neq \emptyset $ . The key ingredients to prove Strichartz estimates are dispersive estimates, energy estimates, interpolation and $TT^*$ arguments. Strichartz estimates for waves inside an arbitrary domain $\Omega $ have been proved by Blair, Smith and Sogge [‘Strichartz estimates for the wave equation on manifolds with boundary’, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), 1817–1829]. We provide a detailed proof of the usual Strichartz estimates from dispersive estimates inside cylindrical convex domains for a certain range of the wave admissibility.

Keywords

dispersive estimatesStrichartz estimateswave equationcylindrical convex domain

MSC classification

Primary: 35L05: Wave equation
Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 2 , April 2023 , pp. 304 - 312
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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