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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access July 15, 2015

Sobolev-Kantorovich Inequalities

  • Michel Ledoux


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.


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Received: 2015-3-7
Accepted: 2015-5-20
Published Online: 2015-7-15

© 2015 Michel Ledoux

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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