A MASS-TRANSPORTATION APPROACH TO SHARP SOBOLEV AND GAGLIARDO-NIRENBERG INEQUALITIES

By Dario Cordero-Erausquin, Bruno Nazaret, Cédric Villani. 2004

385 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4cb71285aebd98613cbab507b270a3ff2f2f137c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

Citations in the corpus

Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm (2004, background): “Two recent articles [9, 10] found the best constants for a class of Gagliardo–Nirenberg inequalities.”
Sharp Gagliardo–Nirenberg Inequalities via p-Laplacian Type Equations (2008, methodology): “And using the solutions to this ODE, the author was able to re-establish the link between mass transport theory and certain Gagliardo–Nirenberg inequalities, first proved in [6].”
Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities (2010, neutral): “ paper by McCann [27] where the displacement convexity issue for some energy functional is reduced to the concavity of det1/N. We also refer to the works of Barthe [2, 3] and Cordero-Erausquin et al. [19]. We require simple pointwise inequalities which are extensions of the classical Jensen’s inequa”
Sharp Constants and Optimizers for a Class of Caffarelli–Kohn–Nirenberg Inequalities (2015, methodology): “The Caffarelli– Kohn–Nirenberg inequalities with arbitrary norms on Euclidean spaces will also be considered in the spirit of Cordero-Erausquin, Nazaret and Villani [13].”
The sharp Sobolev inequality in quantitative form (2009, methodology): “We begin by giving a proof of the Bliss inequality relying on the mass transportation approach of [ CNV ] (see also [LYZ]).”
Mass Transport and Variants of the Logarithmic Sobolev Inequality (2007, background): “For more details about displacement convexity, abovetangent inequalities and applications, see [4, 34, 33, 37, 36, 2, 43, 28].”
Higher-order Sobolev embeddings and isoperimetric inequalities (2013, methodology): “in R, based on mass transportation techniques, has been introduced in [33], and has later been developed in various papers to attack other Sobolev type inequalities, but still in the first-order case.”
Some methods for studying stability in isoperimetric type problems (2008, methodology): “We present here a variant of these arguments, still based on the use of the function τ , and inspired by Gromov’s proof of the isoperimetric inequality [MS, CNV , FiMP].”
Five lectures on optimal transportation: Geometry, regularity and applications (2010, background): “On the pure side, these include connections to inequalities [92] [131] [94] [32] [90] [52], geometry (including sectional [85] [73], Ricci [88] [87] [127] [99] and mean [75] curvature), nonlinear partial differential equations [14] [18] [16] [135] [89], and dynamical systems (weak KAM theory [9]; no”
New approach to the affine P\'olya-Szeg\"o principle and the stability version of the affine Sobolev inequality (2015, background): “[44], and the results of CorderoErausquin, Nazaret and Villani [14] and of Gentil [29].”
IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL (2012, methodology): “We will also use a generalized Stam inequality derived from a general sharp Gagliardo– Nirenberg inequality proved in the remarkable paper of Cordero et al [10].”
Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller–Segel equation (2011, background): “5) is that both inequalities can be proved using ideas coming from the theory of optimal mass transportation [14].”
Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature (2020, background): “We first briefly recall the synthetic notion of nonnegative Ricci curvature introduced by Lott and Villani [42] and Sturm [56, 57].”