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Frank, Rupert L.; 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

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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.

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