Geodesic
Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrödinger equation
Electronic journal of differential equations, Tome 2009 (2009)
In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrodinger equation in all dimensions based on the recent linear profile decomposition result. We then present a new proof of the linear profile decomposition for the Schroindger equation with initial data in the homogeneous Sobolev space; as a consequence, there exists a maximizer for the Sobolev-Strichartz inequality.
Classification : 35Q55
Keywords: maximizers, profile decomposition, Schrödinger equation, Strichartz inequality 
@article{EJDE_2009__2009__a103,
     author = {Shao,  Shuanglin},
     title = {Maximizers for the {Strichartz} and the {Sobolev-Strichartz} inequalities for the {Schr\"odinger} equation},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1173.35692},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a103/}
}
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%J Electronic journal of differential equations
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Shao,  Shuanglin. Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrödinger equation. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a103/