Sharp Sobolev inequalities involving boundary terms

Abstract

Let (M, g) be a compact Riemannian manifold of dimension n (n ≥ 3) with smooth boundary. In [LZ], we established some sharp trace inequality on (M, g). In this paper we establish some sharp Sobolev inequalities using the method in [LZ]. For n ≥ 3, it was shown by Aubin [Au1] and Talenti [T] that, for p = 2n/(n − 2), 1 S 1 = inf R n |∇u| 2 R n |u| p 2/p u… (More)

Cite this paper

@inproceedings{Li1998SharpSI, title={Sharp Sobolev inequalities involving boundary terms}, author={Yanyan Li and Meijun Zhu}, year={1998} }