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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

CiteScore 2017: 0.65

SCImago Journal Rank (SJR) 2017: 1.063
Source Normalized Impact per Paper (SNIP) 2017: 0.833

Mathematical Citation Quotient (MCQ) 2017: 0.86

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Sobolev-Kantorovich Inequalities

Michel Ledoux
  • Corresponding author
  • Institut de Mathématiques de Toulouse, Université de Toulouse–Paul-Sabatier, F-31062 Toulouse, France, and Institut Universitaire de France
  • Other articles by this author:
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Published Online: 2015-07-15 | DOI: https://doi.org/10.1515/agms-2015-0011


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.

Keywords: Interpolation inequality; Sobolev norm; Kantorovich distance; heat flow; Harnack inequality

MSC: Primary: 35K08; 60J60; 58J60; 53C21; Secondary:; 46E35; 35B65


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About the article

Received: 2015-03-07

Accepted: 2015-05-20

Published Online: 2015-07-15

Citation Information: Analysis and Geometry in Metric Spaces, Volume 3, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2015-0011.

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© 2015 Michel Ledoux. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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