A sharp monomial Caffarelli-Kohn-Nirenberg inequality
Abstract
We consider a monomial Caffarelli-Kohn-Nirenberg inequality, find the optimal constant and classify the optimizers under an integrated curvature dimension condition. We take advantage of the $Γ$-calculus to exploit geometrical techniques to tackle the problem and regularity results to justify some integration by parts. A symmetry-breaking result is also provided.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Mathematical Inequalities and Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 27 January 2026
- Document type
- Preprint