Sobolev-Kantorovich Inequalities

Abstract

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
• primary: 35k08
• 60j60
• 58j60
• 53c21
• secondary:
• 46e35
• 35b65