3 years ago

Classification of solutions of an equation related to a conformal log Sobolev inequality. (arXiv:2003.08135v1 [math.AP])

Rupert L. Frank, Tobias König, Hanli Tang
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 to 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.

Publisher URL: http://arxiv.org/abs/2003.08135

DOI: arXiv:2003.08135v1

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