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

Frank, Rupert L. ; König, Tobias und Tang, Hanli (2020): Classification of solutions of an equation related to a conformal log Sobolev inequality. In: Advances in Mathematics, Bd. 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0001-8708
• Sprache: Englisch