Duality and Stability for Functional Inequalities
By Eric A. Carlen. 2016
50 citations recorded by the source corpus.
We develop a general framework for using duality to "transfer" stability results for a functional inequality to its dual inequality. As an application, we prove a stability bound for the Hardy-Littlewood-Sobolev inequality, which is related by duality, and the results proved here, to a stability inequality for the Sobolev inequality proved by Bianchi and Egnell, and extended by Chen, Frank and Weth. We also discuss how the results proved here can be combined with the proof of functional inequalities by means of flows to prove stability bounds with computable constants
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/99399fc374cab0741e5e3cff7188d9e4ad8a3a51
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In Applied Mathematics
- Y. Zhang
- Alessio Figalli
- Guido De Philippis
- Max Fathi
- Dario Trevisan
- Robert J. McCann
- N. Fusco
- Young-Heon Kim
In Control and Systems Engineering
In Mathematical Physics
Citations in the corpus
- Sharp gradient stability for the Sobolev inequality (2020, background): “Introduction Motivated by important applications to problems in the calculus of variations and evolution PDEs, in recent years there has been a growing interest around the understanding of quantitative stability for functional/geometric inequalities, see for instance [3, 2, 8, 27, 28, 21, 9, 22, 29,”