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

Vladimir Georgiev; George Venkov

doi:10.1016/j.jde.2011.04.012

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

Vladimir Georgiev^*, George Venkov

^*Corresponding author for this work

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

14 Citations (Scopus)

Abstract

In the present article we study the radial symmetry and uniqueness 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 obtain symmetry and uniqueness results.

Original language	English
Pages (from-to)	420-438
Number of pages	19
Journal	Journal of Differential Equations
Volume	251
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2011.04.012
Publication status	Published - 2011 Jul 15
Externally published	Yes

Keywords

Hartree equations
Minimizers
Nonlinear solitary waves
Symmetry
Variational methods

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2011.04.012

Cite this

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title = "Symmetry and uniqueness of minimizers of Hartree type equations with external Coulomb potential",

abstract = "In the present article we study the radial symmetry and uniqueness 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 obtain symmetry and uniqueness results.",

keywords = "Hartree equations, Minimizers, Nonlinear solitary waves, Symmetry, Variational methods",

author = "Vladimir Georgiev and George Venkov",

note = "Funding Information: E-mail addresses: georgiev@dm.unipi.it (V. Georgiev), gvenkov@tu-sofia.bg (G. Venkov). 1 The author was supported by the Italian National Council of Scientific Research (project “Analisi nello spazio delle fasi per E.D.P.”.",

year = "2011",

month = jul,

day = "15",

doi = "10.1016/j.jde.2011.04.012",

language = "English",

volume = "251",

pages = "420--438",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Symmetry and uniqueness of minimizers of Hartree type equations with external Coulomb potential

AU - Georgiev, Vladimir

AU - Venkov, George

N1 - Funding Information: E-mail addresses: georgiev@dm.unipi.it (V. Georgiev), gvenkov@tu-sofia.bg (G. Venkov). 1 The author was supported by the Italian National Council of Scientific Research (project “Analisi nello spazio delle fasi per E.D.P.”.

PY - 2011/7/15

Y1 - 2011/7/15

N2 - In the present article we study the radial symmetry and uniqueness 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 obtain symmetry and uniqueness results.

AB - In the present article we study the radial symmetry and uniqueness 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 obtain symmetry and uniqueness results.

KW - Hartree equations

KW - Minimizers

KW - Nonlinear solitary waves

KW - Symmetry

KW - Variational methods

UR - http://www.scopus.com/inward/record.url?scp=79955718491&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955718491&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2011.04.012

DO - 10.1016/j.jde.2011.04.012

M3 - Article

AN - SCOPUS:79955718491

SN - 0022-0396

VL - 251

SP - 420

EP - 438

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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