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arXiv · 1702.03090

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

François Bolley·Dario Cordero-Erausquin·Yasuhiro Fujita·Ivan Gentil·Arnaud Guillin
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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 results by S. Bobkov-M. Ledoux, M. del Pino-J. Dolbeault and B. Nazaret.

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François Bolley, Dario Cordero-Erausquin, Yasuhiro Fujita, Ivan Gentil, Arnaud Guillin. 2017-02-10. New sharp Gagliardo-Nirenberg-Sobolev inequalities and an improved Borell-Brascamp-Lieb inequality. https://arxiv.org/abs/1702.03090

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