Degenerate stability of some Sobolev inequalities

Frank, Rupert L. (2022): Degenerate stability of some Sobolev inequalities. In: Annales De L'Institut Henri Poincaré (C): Non Linear Analysis, Vol. 39, No. 6: pp. 1459-1484

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0294-1449
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 390814868