Differential and Integral Equations

A sharp bilinear estimate for the Klein--Gordon equation in arbitrary space-time dimensions

Chris Jeavons

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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.

Article information

Differential Integral Equations, Volume 27, Number 1/2 (2014), 137-156.

First available in Project Euclid: 12 November 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B45: A priori estimates 35L10: Second-order hyperbolic equations


Jeavons, Chris. A sharp bilinear estimate for the Klein--Gordon equation in arbitrary space-time dimensions. Differential Integral Equations 27 (2014), no. 1/2, 137--156. https://projecteuclid.org/euclid.die/1384282857

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