New Sharp Gagliardo–Nirenberg–Sobolev Inequalities and an Improved Borell–Brascamp–Lieb Inequality. (24th May 2018)

• Record Type: Journal Article
• Authors: Bolley, François; Cordero-Erausquin, Dario; Fujita, Yasuhiro; Gentil, Ivan; Guillin, Arnaud
• Is Part Of: International mathematics research notices. Volume 2020:Number 10(2020)
• Page Start: 3042
• Page End: 3083
• Publication Date: 2018-05-24
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rny111
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: We propose a new Borell–Brascamp–Lieb inequality that leads to novel sharp Euclidean inequalities such as Gagliardo–Nirenberg–Sobolev inequalities in $ {\mathbb{R}}^n$ and in the half-space $ {\mathbb{R}}^n_+$ . This gives a new bridge between the geometric point of view of the Brunn–Minkowski inequality and the functional point of view of the Sobolev-type inequalities. In this way we unify, simplify, and generalize results by S. Bobkov–M. Ledoux, M. del Pino–J. Dolbeault, and B. Nazaret.