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Classification of solutions of an equation related to a conformal log Sobolev inequality

Frank, Rupert L. and König, Tobias and Tang, Hanli (2020) Classification of solutions of an equation related to a conformal log Sobolev inequality. Advances in Mathematics, 375 . Art. No. 107395. ISSN 0001-8708. doi:10.1016/j.aim.2020.107395.

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We classify all finite energy solutions of an equation which arises as the Euler–Lagrange equation of a conformally invariant logarithmic Sobolev inequality on the sphere due to Beckner. Our proof uses an extension of the method of moving spheres from R^n to S^n and a classification result of Li and Zhu. Along the way we prove a small volume maximum principle and a strong maximum principle for the underlying operator which is closely related to the logarithmic Laplacian.

Item Type:Article
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URLURL TypeDescription Paper
Frank, Rupert L.0000-0001-7973-4688
Tang, Hanli0000-0001-8060-9884
Additional Information:© 2020 Elsevier Inc. Received 19 March 2020, Revised 16 August 2020, Accepted 21 August 2020, Available online 3 September 2020. The first author is grateful to M. Zhu for a correspondence in May 2012 on the topic of this paper. Partial support through US National Science Foundation grant DMS-1363432 (R.L.F.), Studienstiftung des Deutschen Volkes (T.K.) and National Natural Science Foundation of China (Grant No. 11701032) (H.T.) is acknowledged.
Funding AgencyGrant Number
Studienstiftung des Deutschen VolkesUNSPECIFIED
National Natural Science Foundation of China11701032
Subject Keywords:Log-Sobolev inequality; Classification of solutions; Conformal invariance; Method of moving spheres
Record Number:CaltechAUTHORS:20200910-141623696
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Official Citation:Rupert L. Frank, Tobias König, Hanli Tang, Classification of solutions of an equation related to a conformal log Sobolev inequality, Advances in Mathematics, Volume 375, 2020, 107395, ISSN 0001-8708, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105313
Deposited By: Tony Diaz
Deposited On:10 Sep 2020 22:06
Last Modified:16 Nov 2021 18:42

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