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

Frank, Rupert L. and Lenzmann, Enno (2009) Uniqueness of ground states for the L^2-critical boson star equation. . (Submitted)

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We establish uniqueness of ground states u(x)≥0 for the L^2-critical boson star equation √−Δu−(|x|^(−1)∗|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.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:Submitted on 19 May 2009. R.L. acknowledges support through DFG grant FR 2664/1-1, NSF grant PHY 06 52854; and E.L. is partially supported by NSF grant DMS-070249 and CTS at ETH Zürich. We thank Joachim Krieger, Mathieu Lewin and Pierre Raphaël for valuable discussions.
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Deutsche Forschungsgemeinschaft (DFG)FR 2664/1-1
Record Number:CaltechAUTHORS:20170526-093631237
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77803
Deposited By: Ruth Sustaita
Deposited On:26 May 2017 17:29
Last Modified:26 May 2017 17:29

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