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

  • Vladimir Georgiev

    Università di Pisa, Dipartimento di Matematica, Largo B. Pontecorvo 5, 56124, Pisa, Italy
  • Francesca Prinari

    Università di Ferrara, Dipartimento di Matematica, via Machiavelli 35, 44100, Ferrara, Italy
  • Nicola Visciglia

    Università di Pisa, Dipartimento di Matematica, Largo B. Pontecorvo 5, 56124, Pisa, Italy

Abstract

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

provided that and is small. The main result shows that minimizers are radially symmetric modulo suitable translation.

Résumé

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

pourvu que et est petit.

Cite this article

Vladimir Georgiev, Francesca Prinari, Nicola Visciglia, On the radiality of constrained minimizers to the Schrödinger–Poisson–Slater energy. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 3, pp. 369–376

DOI 10.1016/J.ANIHPC.2011.12.001