On the radiality of constrained minimizers to the Schrödinger–Poisson–Slater energy
Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 3, pp. 369-376.

We study the radial symmetry of minimizers to the Schrödinger–Poisson–Slater (S–P–S) energy:

inf uH 1 ( 3 ) u L 2 ( 3 ) =ρ1 2 3 |u| 2 +1 4 3 3 |u(x)| 2 |u(y)| 2 |x-y|dxdy-1 p 3 |u| p dx
provided that 2<p<3 and ρ is small. The main result shows that minimizers are radially symmetric modulo suitable translation.

On montre la radialité des minimiseurs de lʼénergie de Schrödinger–Poisson–Slater

inf uH 1 ( 3 ) u L 2 ( 3 ) =ρ1 2 3 |u| 2 +1 4 3 3 |u(x)| 2 |u(y)| 2 |x-y|dxdy-1 p 3 |u| p dx
pourvu que 2<p<3 et ρ est petit.

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     author = {Georgiev, Vladimir and Prinari, Francesca and Visciglia, Nicola},
     title = {On the radiality of constrained minimizers to the {Schr\"odinger{\textendash}Poisson{\textendash}Slater} energy},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {369--376},
     publisher = {Elsevier},
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     year = {2012},
     doi = {10.1016/j.anihpc.2011.12.001},
     zbl = {1260.35204},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2011.12.001/}
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Georgiev, Vladimir; Prinari, Francesca; Visciglia, Nicola. On the radiality of constrained minimizers to the Schrödinger–Poisson–Slater energy. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 3, pp. 369-376. doi : 10.1016/j.anihpc.2011.12.001. http://www.numdam.org/articles/10.1016/j.anihpc.2011.12.001/

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