Degenerate stability of some Sobolev inequalities
Rupert L. Frank
Ludwig-Maximilian Universität München; and Munich Center for Quantum Science and Technology, Germany; California Institute of Technology, Pasadena, USA
Abstract
We show that on 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 . Our proof proceeds by an iterated Bianchi–Egnell strategy.
Cite this article
Rupert L. Frank, Degenerate stability of some Sobolev inequalities. Ann. Inst. H. Poincaré Anal. Non Linéaire 39 (2022), no. 6, pp. 1459–1484
DOI 10.4171/AIHPC/35