Stability inequalities with explicit constants for a family of reverse Sobolev inequalities on the sphere
Abstract
Abstract We prove a stability inequality associated to the reverse Sobolev inequality on the sphere $\mathbb{S}^{n}$ from [13], for the full admissible parameter range $s - \frac{n}{2} \in (0,1) \cup (1,2)$. To implement the classical proof of Bianchi and Egnell [3], we overcome the main difficulty that the underlying operator $A_{2s}$ is not positive definite. As a consequence of our analysis and recent results from [15], the case $s - \frac{n}{2} \in (1,2)$ remarkably constitutes the first example of a Sobolev-type stability inequality (i) whose best constant is explicit and (ii) which does not admit an optimizer.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Harmonic Analysis Research
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 13
- Publication date
- 11 June 2026
- Language
- EN