Maximizers for the Strichartz Inequality

By Damiano Foschi. 2004

150 citations recorded by the source corpus.

We compute explicitly the best constants and, by solving some functional equations, we find all maximizers for homogeneous Strichartz estimates for the Schrodinger equation and for the wave equation in the cases when the Lebesgue exponent is an even integer

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b12fa2a8bb624dbe86f4b70f5fa9f410b710c86c

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On sharp Strichartz inequalities in low dimensions (2006, methodology): “Very recently, Damiano Foschi [3] gave a simple proof of the Strichartz inequality in one and two dimensions, which yields the sharp constant.”
A Sharp Inequality for the Strichartz Norm (2008, methodology): “In the same spirit, sharp restriction/extension inequalities for the cone are implicit in Foschi’s work [4] for the wave equation.”
Maximizers for the Strichartz Inequalities for the wave equation (2009, background): “Subsequently, Foschi [7], working in dimensions 1 and 2, explicitly determined the sharp constants, and characterized the maximizers for the Strichartz inequality for both the Schrödinger and wave equations.”
Global Maximizers for the Sphere Adjoint Fourier Restriction Inequality (2013, result): “In order to find maximizers for (1), we follow the spirit of the proof of analogous results obtained by the author for the paraboloid and the cone [4].”
The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality (2008, methodology): “t∂3xRe(e−i(·)anφ)k L6 t,x = SR airy, SC schr = 2 1/231/6SR airy. Remark 1.10. Note that when SC schr = 3 1/6SC airyor SC schr = 2 1/231/6SR airy, the explicit φ had been uniquely determined by Foschi [9] and Hundertmark-Zharnitsky [10] independently: they are Gaussians up to the natural symmetries e”
Existence of Extremals for a Fourier Restriction Inequality (2010, background): “Such equalities are the key to one proof [Foschi 2007] that Gaussians are extremal for P2.”
On the existence of maximizers for a family of restriction theorems (2010, background): “but this is absurd since, by [3], there are no maximizers for (2.”
A refinement of the Strichartz inequality for the wave equation with applications (2012, background): “This was known for d = 2, 3 for which the maximizers were calculated explicitly [22].”
Existence of maximizers for Sobolev–Strichartz inequalities (2011, background): “[6] D. Foschi, Maximizers for the Strichartz inequality, J. Eur.”
Heat-flow monotonicity of Strichartz norms (2008, background): “Recently Foschi [ 9 ] and independently Hundertmark and Zharnitsky [10] showed that in the cases where one can \multiply out" the Strichartz norm”
Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrödinger equation (2009, methodology): “[7] D. Foschi.”
Maximizers for the Stein–Tomas Inequality (2016, unknown): “We cite the following conjecture from [14]; see also [21].”
The geodesic X-ray transform with fold caustics (2010, background): “Such equalities are the key to one proof [Foschi 2007] that Gaussians are extremal for P2.”