Remarks on the sharp constant for the Schrodinger Strichartz estimate and applications

Abstract

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 $L^2$-critical case $p=1+4/n$.

Keywords

• Strichartz estimate
• optimal constant
• Schrodinger equation
• restriction inequality