Published July 24, 2021
| Submitted
Discussion Paper
Open
Degenerate stability of some Sobolev inequalities
- Creators
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Frank, Rupert L.
Chicago
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Abstract
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.
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.Attached Files
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Additional details
- Eprint ID
- 111521
- Resolver ID
- CaltechAUTHORS:20211018-185230397
- NSF
- DMS-1363432
- NSF
- DMS-1954995
- Deutsche Forschungsgemeinschaft (DFG)
- EXC-2111-390814868
- Created
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2021-11-03Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field