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Sharp Sobolev trace inequalities on Riemannian manifolds with boundaries

✍ Scribed by Yanyan Li; Meijun Zhu

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
264 KB
Volume
50
Category
Article
ISSN
0010-3640

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✦ Synopsis

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, ( βˆ‚M |u| q dsg) 2/q ≀ S M |βˆ‡gu| 2 dvg + A βˆ‚M u 2 dsg, for all u ∈ H 1 (M ). The inequality is sharp in the sense that the inequality is false when S is replaced by any smaller number.

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