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- W4385890384 abstract "We show that the Caffarelli-Kohn-Nirenberg (CKN) inequality holds with a remainder term that is quartic in the distance to the set of optimizers for the full parameter range of the Felli-Schneider (FS) curve. The fourth power is best possible. This is due to the presence of non-trivial zero modes of the Hessian of the deficit functional along the FS-curve. Following an iterated Bianchi-Egnell strategy, the heart of our proof is verifying a `secondary non-degeneracy condition'. Our result completes the stability analysis for the CKN-inequality to leading order started by Wei and Wu. Moreover, it is the first instance of degenerate stability for non-constant optimizers and for a non-compact domain." @default.
- W4385890384 created "2023-08-17" @default.
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- W4385890384 date "2023-08-15" @default.
- W4385890384 modified "2023-09-27" @default.
- W4385890384 title "Degenerate Stability of the Caffarelli-Kohn-Nirenberg Inequality along the Felli-Schneider Curve" @default.
- W4385890384 doi "https://doi.org/10.48550/arxiv.2308.07917" @default.
- W4385890384 hasPublicationYear "2023" @default.
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