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Article Dans Une Revue International Mathematics Research Notices Année : 2020

New sharp Gagliardo-Nirenberg-Sobolev inequalities and an improved Borell-Brascamp-Lieb inequality

Résumé

We propose a new Borell-Brascamp-Lieb inequality which leads to novel sharp Euclidean inequalities such as Gagliardo-Nirenberg-Sobolev inequalities in R^n and in the half-space R^n_+. This gives a new bridge between the geometric pont 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.
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Dates et versions

hal-01464530 , version 1 (10-02-2017)
hal-01464530 , version 2 (24-01-2018)
hal-01464530 , version 3 (03-05-2018)

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Citer

François Bolley, Dario Cordero-Erausquin, Yasuhiro Fujita, Ivan Gentil, Arnaud Guillin. New sharp Gagliardo-Nirenberg-Sobolev inequalities and an improved Borell-Brascamp-Lieb inequality. International Mathematics Research Notices, In press, 2020 (10), pp.3042-3083. ⟨10.1093/imrn/rny111⟩. ⟨hal-01464530v3⟩
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