Kawohl, Bernd; Krömer, Stefan Uniqueness and symmetry of minimizers of Hartree type equations with external Coulomb potential. (English) Zbl 1255.35023 Adv. Calc. Var. 5, No. 4, 427-432 (2012). Summary: In a recent paper, V. Georgiev and G. Venkov [J. Differ. Equations 251, No. 2, 420–438 (2011; Zbl 1219.35086)] establish first radial symmetry and then uniqueness of minimizers to a certain functional. In the present paper we prove first the uniqueness of possible positive minimizers by revealing a hidden convexity property of the underlying functional. Then symmetry follows from the simple observation that uniqueness fails if there is a nonradial minimizer, because it could be rotated and give rise to a second minimizer. Cited in 4 Documents MSC: 35B06 Symmetries, invariants, etc. in context of PDEs 35B09 Positive solutions to PDEs 35J20 Variational methods for second-order elliptic equations 35Q40 PDEs in connection with quantum mechanics Keywords:nonlocal elliptic PDE; hidden convexity Citations:Zbl 1219.35086 PDFBibTeX XMLCite \textit{B. Kawohl} and \textit{S. Krömer}, Adv. Calc. Var. 5, No. 4, 427--432 (2012; Zbl 1255.35023) Full Text: DOI