In this paper, we establish some sharp Sobolev trace inequalities on n-dimensional, compact Riemannian manifolds with smooth boundaries. More specifically, let We establish for any Riemannian manifold with a smooth boundary, denoted as (M, g), that there exists some constant A = A(M, g) > 0, ( βM |
A sharp Sobolev inequality on Riemannian manifolds
β Scribed by Yan Yan Li; Tonia Ricciardi
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 71 KB
- Volume
- 335
- Category
- Article
- ISSN
- 1631-073X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let (M, g) be a smooth compact Riemannian N-manifold, N 2, let p # (1, N) real, and let H p 1 (M) be the Sobolev space of order p involving first derivatives of the functions. By the Sobolev embedding theorem, H p 1 (M)/L p\* (M) where p\*=NpΓ(N& p). Classically, this leads to some Sobolev inequalit
We obtain a log-Sobolev inequality with a neat and explicit potential for the gradient on a based loop space over a compact Riemannian manifold. The potential term relies only on the curvature of the manifold and the Hessian of the heat kernel, and is L p -integrable for all p 1. The log-Sobolev ine
We study the second best constant problem for logarithmic Sobolev inequalities on complete Riemannian manifolds and investigate its relationship with optimal heat kernel bounds and the existence of extremal functions.
Let N 5, a > 0, be a smooth bounded domain in We prove there exists an Ξ± 0 > 0 such that, for all u β H 1 ( )
We establish a generalization to Riemannian manifolds of the Caffarelli-Kohn-Nirenberg inequality. The applied method is based on the use of conformal Killing vector fields and E. Mitidieri's approach to Hardy inequalities.