On the geometric dependence of Riemannian Sobolev best constants
Differential Geometry
2008-08-11 v2 Analysis of PDEs
Abstract
We concerns here with the continuity on the geometry of the second Riemannian L^p-Sobolev best constant B_0(p,g) associated to the AB program. Precisely, for 1 <= p <= 2, we prove that B_0(p,g) depends continuously on g in the C^2-topology. Moreover, this topology is sharp for p = 2. From this discussion, we deduce some existence and C^0-compactness results on extremal functions.
Keywords
Cite
@article{arxiv.0708.2376,
title = {On the geometric dependence of Riemannian Sobolev best constants},
author = {Ezequiel R. Barbosa and Marcos Montenegro},
journal= {arXiv preprint arXiv:0708.2376},
year = {2008}
}
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19 pages