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

Vladimir Georgiev; Francesca Prinari; Nicola Visciglia

doi:10.1016/j.anihpc.2011.12.001

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

Vladimir Georgiev^*, Francesca Prinari, Nicola Visciglia

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

We study the radial symmetry of minimizers to the Schrödinger-Poisson- Slater (S-P-S) energy:infu ε^H1(^R3) ∥u∥^L2(^R3)=ρ12∫^R3|Δu| ²+14∫^R3∫^R3|^u(x)|2| ^u(y)|2|x-y|dxdy-1p∫^R3|^u|pdx provided that 2<p<3 and ρ is small. The main result shows that minimizers are radially symmetric modulo suitable translation.

Original language	English
Pages (from-to)	369-376
Number of pages	8
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	29
Issue number	3
DOIs	https://doi.org/10.1016/j.anihpc.2011.12.001
Publication status	Published - 2012
Externally published	Yes

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2011.12.001

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abstract = "We study the radial symmetry of minimizers to the Schr{\"o}dinger-Poisson- Slater (S-P-S) energy:infu εH1(R3) ∥u∥L2(R3)=ρ12∫R3|Δu| 2+14∫R3∫R3|u(x)|2| u(y)|2|x-y|dxdy-1p∫R3|u|pdx provided that 2",

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doi = "10.1016/j.anihpc.2011.12.001",

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AU - Georgiev, Vladimir

AU - Prinari, Francesca

AU - Visciglia, Nicola

PY - 2012

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AB - We study the radial symmetry of minimizers to the Schrödinger-Poisson- Slater (S-P-S) energy:infu εH1(R3) ∥u∥L2(R3)=ρ12∫R3|Δu| 2+14∫R3∫R3|u(x)|2| u(y)|2|x-y|dxdy-1p∫R3|u|pdx provided that 2

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ER -

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

Abstract

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