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

Frank, Rupert L. and Lenzmann, Enno (2010) On ground states for the L^2-critical boson star equation. . (Submitted)

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We consider ground state solutions u ⩾ 0 for the L^2-critical boson star equation √−u − (|x|^(−1) ∗ |u|^2)u = −u in R^3. 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 L^2-critical boson star equation in R^3, but the arguments given there contained a gap. However, we refer to our recent preprint [FraLe] in 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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Additional Information:© 2010 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. (Submitted on 14 Oct 2009 (v1), last revised 26 Oct 2010 (this version, v2) R. F. gratefully acknowledges support through DFG grant FR 2664/1-1 and NSF grant PHY 06 52854. E. L. is supported by a Steno fellowship of the Danish research council and NSF grant DMS-0702492.
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Deutsche Forschungsgemeinschaft (DFG)FR 2664/1-1
Danish Research CouncilUNSPECIFIED
Record Number:CaltechAUTHORS:20170526-101905288
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ID Code:77810
Deposited By: Ruth Sustaita
Deposited On:26 May 2017 19:03
Last Modified:26 May 2017 19:03

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