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

Frank, Rupert L.; König, Tobias; 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
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0001-8708
• Language: English