A Sharp Sobolev--Strichartz estimate for the wave equation

Abstract

We calculate the the sharp constant and characterise 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 space dimensions.

8 pages, no figures

References in corpus (2)

• A sharp bilinear estimate for the Klein-Gordon equation in arbitrary space-time dimensions
• Optimal constants and extremisers for some smoothing estimates