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. https://resolver.caltech.edu/CaltechAUTHORS:20200910-141623696
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Abstract
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.
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| 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. | |||||||||
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| Subject Keywords: | Log-Sobolev inequality; Classification of solutions; Conformal invariance; Method of moving spheres | |||||||||
| DOI: | 10.1016/j.aim.2020.107395 | |||||||||
| Record Number: | CaltechAUTHORS:20200910-141623696 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200910-141623696 | |||||||||
| 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, https://doi.org/10.1016/j.aim.2020.107395. (http://www.sciencedirect.com/science/article/pii/S0001870820304230) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 105313 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 10 Sep 2020 22:06 | |||||||||
| Last Modified: | 16 Nov 2021 18:42 |
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