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, p. 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.

@article{AIHPC_2012__29_3_369_0,
     author = {Georgiev, Vladimir and Prinari, Francesca and Visciglia, Nicola},
     title = {On the radiality of constrained minimizers to the Schr\"odinger--Poisson--Slater energy},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {29},
     number = {3},
     year = {2012},
     pages = {369-376},
     doi = {10.1016/j.anihpc.2011.12.001},
     zbl = {1260.35204},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2012__29_3_369_0}
}
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/item/AIHPC_2012__29_3_369_0/

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