ORCID: https://orcid.org/0000-0001-7973-4688; König, Tobias and Tang, Hanli
(2020):
Classification of solutions of an equation related to a conformal log Sobolev inequality.
In: Advances in Mathematics, Vol. 375, 107395
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.
Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics |
Subjects: | 500 Science > 510 Mathematics |
ISSN: | 0001-8708 |
Language: | English |
Item ID: | 88935 |
Date Deposited: | 25. Jan 2022, 09:28 |
Last Modified: | 13. Aug 2024, 12:44 |