On ground states for the L²-critical boson star equation

2009/10/14 by Frank, Rupert L., Lenzmann, Enno · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0910.2721

Abstract

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.

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