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January/February 2014 A sharp bilinear estimate for the Klein--Gordon equation in arbitrary space-time dimensions
Chris Jeavons
Differential Integral Equations 27(1/2): 137-156 (January/February 2014).

Abstract

We prove a sharp bilinear inequality for the Klein--Gordon equation on $\mathbb{R}^{d+1}$, for any $d \geq 2$. This extends work of Ozawa--Rogers and Quilodrán for the Klein--Gordon equation and generalizes work of Bez--Rogers for the wave equation. As a consequence, we obtain a sharp Strichartz estimate for the solution of the Klein--Gordon equation in five spatial dimensions for data belonging to $H^1$. We show that maximizers for this estimate do not exist and that any maximizing sequence of initial data concentrates at spatial infinity.

Citation

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Chris Jeavons. "A sharp bilinear estimate for the Klein--Gordon equation in arbitrary space-time dimensions." Differential Integral Equations 27 (1/2) 137 - 156, January/February 2014.

Information

Published: January/February 2014
First available in Project Euclid: 12 November 2013

zbMATH: 1313.35036
MathSciNet: MR3161599

Subjects:
Primary: 35B45, 35L10

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 1/2 • January/February 2014
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