On the radiality of constrained minimizers to the Schrödinger–Poisson–Slater energy

We study the radial symmetry of minimizers to the Schrödinger–Poisson–Slater (S–P–S) energy:infu∈H1(R3)‖u‖L2(R3)=ρ12∫R3|∇u|2+14∫R3∫R3|u(x)|2|u(y)|2|x−y|dxdy−1p∫R3|u|pdx provided that 2

RésuméOn montre la radialité des minimiseurs de lʼénergie de Schrödinger–Poisson–Slaterinfu∈H1(R3)‖u‖L2(R3)=ρ12∫R3|∇u|2+14∫R3∫R3|u(x)|2|u(y)|2|x−y|dxdy−1p∫R3|u|pdx pourvu que 2