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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01464530
Contributor : Ivan Gentil <>
Submitted on : Thursday, May 3, 2018 - 4:53:06 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:58 PM

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  • HAL Id : hal-01464530, version 3

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François Bolley, Dario Cordero-Erausquin, Yasuhiro Fujita, Ivan Gentil, Arnaud Guillin. New sharp Gagliardo-Nirenberg-Sobolev inequalities and an improved Borell-Brascamp-Lieb inequality. 2017. ⟨hal-01464530v3⟩

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