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Article Dans Une Revue Advances in Mathematics Année : 2020

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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hal-03505330 , version 1 (30-12-2021)

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Rupert Frank, Tobias König, Hanli Tang. Classification of solutions of an equation related to a conformal log Sobolev inequality. Advances in Mathematics, 2020, 375, pp.107395. ⟨10.1016/j.aim.2020.107395⟩. ⟨hal-03505330⟩
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