2009/10/14 by Rupert L. Frank, Enno Lenzmann, Frank, Rupert L. +1 · 26 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Astrophysics #Black Holes and Theoretical Physics #Boson #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical physics #Physics #Quantum mechanics #Star (game theory) #math-ph #math.AP #math.MP
paper · pdf · doi:10.48550/arxiv.0910.2721
published in arXiv (Cornell University) (Cornell University) · Replaced version; see also http://arxiv.org/abs/1009.4042
openalex publication_date 2009/10/14 · arxiv created 2010/10/26 · arxiv updated 2010/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We consider ground state solutions u ≥ 0 for the L2-critical boson star equation √(-Δ) u - (|x|-1 ∗ |u|2 ) u = -u in \R3. We prove analyticity and radial symmetry of u. In a previous version of this paper, we also stated uniqueness and nondegeneracy of ground states for the L2-critical boson star equation in \R3, but the arguments given there contained a gap. However, we refer to our recent preprint \citeFraLe in \tt arXiv:1009.4042, where we prove a general uniqueness and nondegeneracy result for ground states of nonlinear equations with fractional Laplacians in d=1 space dimension.