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

被引：5

作者：

Bolley, Francois ^{[1
]}

Cordero-Erausquin, Dario ^{[2
]}

Fujita, Yasuhiro ^{[3
]}

Gentil, Ivan ^{[4
]}

Guillin, Arnaud ^{[5
]}

机构：

[1] Sorbonne Univ Paris 6, Lab Probabilites Stat & Modelisat, UMR CNRS 8001, Paris, France

[2] Sorbonne Univ Paris 6, Inst Math Jussieu, UMR CNRS 7586, Paris, France

[3] Univ Toyama, Dept Math, Tomaya 9308555, Japan

[4] Univ Lyon, Univ Claude Bernard Lyon 1, UMR CNRS 5208, Inst Camille Jordan, Lyon, France

[5] Univ Clermont Auvergne, Lab Math Blaise Pascal, UMR CNRS 6620, Clermont Ferrand, France

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2020年 / 2020卷 / 10期

关键词：

BRUNN-MINKOWSKI; LOGARITHMIC SOBOLEV;

D O I：

10.1093/imrn/rny111

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We propose a new Borell-Brascamp-Lieb inequality that leads to novel sharp Euclidean inequalities such as Gagliardo-Nirenberg-Sobolev inequalities in and in the half-space . 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.

引用

页码：3042 / 3083

页数：42

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