In this article, we compute the sharp constant for the homogeneous Schrodinger Strichartz inequality, and for the Fourier restriction inequality on the paraboloid in any dimension under the condition conjectured (and proved for dimensions 1 and 2) that the maximizers are Gaussians. We observe also how this would imply a far from optimal, but "cheap" and sufficient, criterion of the global wellposedness in the -critical case .
Submitted October 14, 2014. Published October 21, 2015.
Math Subject Classifications: 35Q41, 35A23.
Key Words: Strichartz estimate; optimal constant; Schrodinger equation; restriction inequality.
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| Alessandro Selvitella |
Department of Mathematics & Statistics
McMaster University, Hamilton Hall, Office 401HH
1280 Main Street West, Hamilton, Ontario, Canada L8S 4K1
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