Symmetry and uniqueness of minimizers of Hartree type equations with external Coulomb potential

2010/08/23 by Vladimir Georgiev, Georgiev, Vladimir, George Venkov +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.1008.3871

openalex publication_date 2010/08/23 · arxiv created 2010/12/08 · arxiv updated 2010/12/10 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In the present article we study the radial symmetry of minimizers of the energy functional, corresponding to the repulsive Hartree equation in external Coulomb potential. To overcome the difficulties, resulting from the "bad" sign of the nonlocal term, we modify the reflection method and then, by using Pohozaev integral identities we get the symmetry result.

Citations

• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• A symmetry problem in potential theory
• Orbital stability of standing waves for some nonlinear Schr�dinger equations

Cited by

• Some exact solutions of the Schrödinger--Poisson system in spaces of constant sectional curvature

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