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
Degenerate stability of some Sobolev inequalities cover
Download PDF

This article is published open access under our Subscribe to Open model.

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