Sobolev-Kantorovich Inequalities

• Autorzy: Michel Ledoux
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 35K08: Heat kernel
• 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
• 60J60: Diffusion processes
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 35B65: Smoothness and regularity of solutions
• 58J60: Relations with special manifold structures (Riemannian, Finsler, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-03-07

zaakceptowano

2015-05-20

online

2015-07-15

Twórcy

autor

Michel Ledoux

• Institut de Mathématiques de Toulouse, Université de Toulouse–Paul-Sabatier, F-31062 Toulouse, France, and Institut Universitaire de France

Bibliografia

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Identyfikatory

DOI

10.1515/agms-2015-0011