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Published May 26, 2017 | Submitted
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Uniqueness of ground states for the L^2-critical boson star equation

Abstract

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.

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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Additional details

Created:
August 20, 2023
Modified:
October 25, 2023