On a Sharp Sobolev‐Type Inequality on Two-Dimensional Compact Manifolds
✍ Scribed by Margherita Nolasco; Gabriella Tarantello
- Publisher
- Springer
- Year
- 1998
- Tongue
- English
- Weight
- 236 KB
- Volume
- 145
- Category
- Article
- ISSN
- 0003-9527
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📜 SIMILAR VOLUMES
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, ( ∂M |
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\*=NpÂ(N& p). Classically, this leads to some Sobolev inequalit