Sobolev-Kantorovich Inequalities

Michel Ledoux
2015 Analysis and Geometry in Metric Spaces  
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
more » ... nnian manifolds by means of heat flows and Harnack inequalities.
doi:10.1515/agms-2015-0011 fatcat:wkbbicwtyzh23pmepbgslam2ka