Uniqueness of ground states for the L^2-critical boson star equation

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dc.creatorFrank, Rupert L.
dc.creatorLenzmann, Enno
dc.date2009-05-19
dc.date.accessioned2026-07-07T13:16:30Z
dc.date.available2026-07-07T13:16:30Z
dc.descriptionWe establish uniqueness of ground states $u(x) \geq 0$ for the $L^2$-critical boson star equation $\sqrt{-Δ} u - (|x|^{-1} \ast |u|^2) u = -u$ in $\R^3$. The proof blends variational arguments with the harmonic extension to the halfspace $\R^4_+$. Apart from uniqueness, we also show radiality of ground states (up to translations) and the nondegeneracy of the linearization. Our results provide an indispensable basis for the blowup analysis of the time-dependent $L^2$-critical boson star equation. The uniqueness proof can be generalized to different fractional Laplacians $(-Δ)^s$ and space dimensions.
dc.descriptionResearch announcement note; submitted for publication
dc.identifierhttps://arxiv.org/abs/0905.3105
dc.identifierhttp://arxiv.org/abs/0905.3105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/230810
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.titleUniqueness of ground states for the L^2-critical boson star equation
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