New Sharp Gagliardo–Nirenberg–Sobolev Inequalities and an Improved Borell–Brascamp–Lieb Inequality

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–Minkows...

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Bibliographic Details
Published in:International mathematics research notices 2020-05, Vol.2020 (10), p.3042-3083
Main Authors: Bolley, François, Cordero-Erausquin, Dario, Fujita, Yasuhiro, Gentil, Ivan, Guillin, Arnaud
Format: Article
Language:English
Subjects:
Mathematics
Probability
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Summary: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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rny111