New sharp Gagliardo-Nirenberg-Sobolev inequalities and an improved Borell-Brascamp-Liebinequality
Authors: François Bolley, Dario Cordero-Erausquin, Yasuhiro Fujita, Ivan Gentil, Arnaud Guillin
Summary: We suggest a brand new Borell-Brascamp-Lieb inequality which ends up in novel sharp Euclidean inequalities equivalent to Gagliardo-Nirenberg-Sobolev inequalities in R^n and within the half-space R^n_+. This provides a brand new bridge between the geometric pont of view of the Brunn-Minkowski inequality and the useful perspective of the Sobolev kind inequalities. On this means we unify, simplify and outcomes by S. Bobkov-M. Ledoux, M. del Pino-J. Dolbeault and B. Nazaret