A sharp inequality for Sobolev functions
✍ Scribed by Pedro M Girão
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 58 KB
- Volume
- 334
- Category
- Article
- ISSN
- 1631-073X
No coin nor oath required. For personal study only.
✦ Synopsis
Let N 5, a > 0, be a smooth bounded domain in
We prove there exists an α 0 > 0 such that, for all u ∈ H 1 ( )
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## Abstract The best constant and extremal functions for Sobolev trace inequalities on fractional Sobolev spaces are achieved by a simple argument. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
In this paper, we establish some general forms of sharp Sobolev inequalities on the upper half space or any compact Riemannian manifold with smooth boundary. These forms extend some previous results Escobar [11], Li and Zhu [18].
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 |