Published December 2, 2020
| Submitted
Journal Article
Open
Classification of solutions of an equation related to a conformal log Sobolev inequality
- Creators
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Frank, Rupert L.
- König, Tobias
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Tang, Hanli
Chicago
An error occurred while generating the citation.
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.
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.Attached Files
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Additional details
- Eprint ID
- 105313
- DOI
- 10.1016/j.aim.2020.107395
- Resolver ID
- CaltechAUTHORS:20200910-141623696
- NSF
- DMS-1363432
- Studienstiftung des Deutschen Volkes
- National Natural Science Foundation of China
- 11701032
- Created
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2020-09-10Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field