Sharp k-order Sobolev inequalities in the hyperbolic space ${\Bbb H}^n$
Analysis of PDEs
2013-10-01 v2 Differential Geometry
Abstract
In this paper, we obtain the sharp -th order Sobolev inequalities in the hyperbolic space {\H}^n for all . This gives an answer to an open question raised by Aubin in [5, p.176-177] for W^{k,2}({\H}^n) with . In addition, we prove that the associated Sobolev constants are optimal.
Cite
@article{arxiv.0708.0269,
title = {Sharp k-order Sobolev inequalities in the hyperbolic space ${\Bbb H}^n$},
author = {Genqian Liu},
journal= {arXiv preprint arXiv:0708.0269},
year = {2013}
}
Comments
20 pages