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Degenerate stability of some Sobolev inequalities

Frank, Rupert L. (2021) Degenerate stability of some Sobolev inequalities. . (Unpublished)

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We show that on S¹(1/√(d−2)) × S^(d−1)(1) the conformally invariant Sobolev inequality 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 motivated by work of Engelstein, Neumayer and Spolaor. A similar phenomenon arises for subcritical Sobolev inequalities on S^d. Our proof proceeds by an iterated Bianchi-Egnell strategy.

Item Type:Report or Paper (Discussion Paper)
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Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2021 by the author. This paper may be reproduced, in its entirety, for non-commercial purposes. The author wishes to thank R. Neumayer for several discussions on the topic of this paper and her seminar talk in January 2021 at Caltech which motivated this work. J. Dolbeault’s help with references is much appreciated. Partial support through US National Science Foundation grants DMS-1363432 and DMS-1954995 and through German Research Foundation grant EXC-2111-390814868 is acknowledged.
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Deutsche Forschungsgemeinschaft (DFG)EXC-2111-390814868
Record Number:CaltechAUTHORS:20211018-185230397
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111521
Deposited By: George Porter
Deposited On:03 Nov 2021 19:26
Last Modified:03 Nov 2021 19:26

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