A sharp Sobolev-Strichartz estimate for the wave equation

Neal Bez; Chris Jeavons

doi:10.3934/era.2015.22.46

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2015, Volume 22: 46-54. Doi: 10.3934/era.2015.22.46 open access

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A sharp Sobolev-Strichartz estimate for the wave equation

Neal Bez^1, and
Chris Jeavons^2,

1.
Department of Mathematics, Graduate School of Science and Engineering, Saitama University, Saitama 338-8570
2.
School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT

Received: May 31, 2014

Revised: May 31, 2015

Published: December 2014

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Abstract

We calculate the the sharp constant and characterize the extremal initial data in $\dot{H}^{\frac{3}{4}} \times \dot{H}^{-\frac{1}{4}}$ for the $L^4$ Sobolev--Strichartz estimate for the wave equation in four spatial dimensions.

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Mathematics Subject Classification: Primary 35B45; Secondary 35L05.

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References

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