A Sharp Inequality for the Strichartz Norm
By Emanuel Carneiro. 2008
83 citations recorded by the source corpus.
Let be the solution of the linear Schrodinger equationIn the first part of this paper, we obtain a sharp inequality for the Strichartz norm , where , and , that admits only Gaussian maximizers. As corollaries, we obtain sharp forms of the classical Strichartz inequalities in low dimensions (works of Foschi [4] and Hundertmark-Zharnitsky [6]) and also sharp forms of some Sobolev-Strichartz inequalities. In the second part of the paper, we express Foschi's [4] sharp inequalities for the Schrodinger and wave equations in the broader setting of sharp restriction/extension estimates for the paraboloid and the cone.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/dfd9d8b0cf665fea325b1ac9fe1fda4b4a38b448
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Plamen Stefanov
- J. Ramos
- Shuanglin Shao
- Gunther Uhlmann
- Michael Christ
- Aynur Bulut
- William Beckner
- Carlos E. Kenig
In Mathematical Physics
- Gunther Uhlmann
- Plamen Stefanov
- J. Ramos
- Shuanglin Shao
- Michael Christ
- Aynur Bulut
- William Beckner
- Carlos E. Kenig
Citations in the corpus
- Existence of Extremals for a Fourier Restriction Inequality (2010, background): “Several papers have subsequently dealt with related problems, in some cases determining all extremizers explicitly [Foschi 2007; Hundertmark and Zharnitsky 2006; Bennett et al. 2009; Carneiro 2009], in other cases merely proving existence [Shao 2009].”
- Functionals for multilinear fractional embedding (2014, methodology): “Part of this inequality was already used in Carneiro’s thesis (see pages 3133-3134 in [15]).”
- The geodesic X-ray transform with fold caustics (2010, background): “Several papers have subsequently dealt with related problems, in some cases determining all extremizers explicitly [Foschi 2007; Hundertmark and Zharnitsky 2006; Bennett et al. 2009; Carneiro 2009], in other cases merely proving existence [Shao 2009].”
- A refinement of the Strichartz inequality for the wave equation with applications (2012, background): “For progress on closely related problems see [3], [7], [9], [11,12], [18], [19], [20], [27], [43], [49], [53] and [54].”
- Maximizers for the Strichartz Inequalities for the wave equation (2009, methodology): “Related to this literature, following the arguments in [10], Carneiro [6] obtained a sharp inequality for the Strichartz norm,”
- The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality (2008, unknown): “Hence these sequences”
- Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrödinger equation (2009, methodology): “... showed that maximizers exist by an elaborate concentration-compactness method; when d = 1,2, Foschi [7] explicitly determined the best constants and showed that the only maximizers are Gaussians by using the sharp Cauchy-Schwarz inequality and the space-time Fourier transform; Hundertmark and Zh”