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Frank, Rupert L. ORCID logoORCID: https://orcid.org/0000-0001-7973-4688 (2022): Degenerate stability of some Sobolev inequalities. In: Annales De L'Institut Henri Poincaré (C): Non Linear Analysis, Bd. 39, Nr. 6: S. 1459-1484

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Abstract

./ Abstract. We show that on S1(1= d -2) x Sd-1(1) the conformally invariant Sobolev inequal-ity holds with a remainder term that is the fourth power of the distance to the optimizers. The fourth power is best possible. This is in contrast to the more usual vanishing to second order and is moti-vated by work of Engelstein, Neumayer and Spolaor. A similar phenomenon arises for subcritical Sobolev inequalities on Sd. Our proof proceeds by an iterated Bianchi-Egnell strategy.

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