Classification of solutions of an equation related to a conformal log Sobolev inequality
Résumé
We classify all nite energy solutions of an equation which arises as the EulerLagrange 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 classication 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.
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