New Sharp Gagliardo–Nirenberg–Sobolev Inequalities and an Improved Borell–Brascamp–Lieb Inequality. (24th May 2018) - Bolley, François; Cordero-Erausquin, Dario; Fujita, Yasuhiro; Gentil, Ivan; Guillin, Arnaud
Abstract: We propose a new Borell–Brascamp–Lieb inequality that 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 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.