Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrödinger equation

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Existence of maximizers for Sobolev–Strichartz inequalities (2011, methodology): “We also mention the papers by Shao [14] for the Schödinger equation and by Bulut [3] for the wave equation, in which the existence of maximizers for anisotropic Strichartz estimates in spaces LptL q x, for general couples (p, q), is also proved.”
A refinement of the Strichartz inequality for the wave equation with applications (2012, methodology): “For progress on closely related problems see [3], [7], [9], [11,12], [18], [19], [20], [27], [43], [49], [53] and [54].”
On the existence of maximizers for a family of restriction theorems (2010, methodology): “The main tool in [6] is the profile decomposition of bounded sequences in L(2).”
The geodesic X-ray transform with fold caustics (2010, background): “A powerful result [Shao 2009] that leads easily to existence of extremizers is the profile decomposition; see [Bégout and Vargas 2007].”
Existence of Extremals for a Fourier Restriction Inequality (2010, background): “A powerful result [Shao 2009] that leads easily to existence of extremizers is the profile decomposition; see [Bégout and Vargas 2007].”