Geodesic
Sobolev-Kantorovich Inequalities
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means of heat flows and Harnack inequalities.
Mots-clés : Interpolation inequality, Sobolev norm, Kantorovich distance, heat flow, Harnack inequality 
@article{AGMS_2015_3_1_a14,
     author = {Ledoux, Michel},
     title = {Sobolev-Kantorovich {Inequalities}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2015},
     volume = {3},
     number = {1},
     zbl = {1326.35171},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a14/}
}
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Ledoux, Michel. Sobolev-Kantorovich Inequalities. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a14/