On the geometric dependence of Riemannian Sobolev best constants

Ezequiel R. Barbosa; Marcos Montenegro

doi:10.3934/cpaa.2009.8.1759

Article Contents

2009, Volume 8, Issue 6: 1759-1777. Doi: 10.3934/cpaa.2009.8.1759

This issue Previous Article Multiplicity of solutions for elliptic systems via local Mountain Pass method Next Article Low dimensional instability for semilinear and quasilinear problems in $\mathbb{R}^N$

On the geometric dependence of Riemannian Sobolev best constants

Ezequiel R. Barbosa^1, and
Marcos Montenegro^1,

1.
Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, MG

Received: August 31, 2008

Revised: January 31, 2009

Published: October 2009

Abstract Related Papers Cited by

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 $1 \leq p \leq 2$, 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:

Mathematics Subject Classification: 32Q10, 53C21.

Citation:

Article Metrics

HTML views() PDF downloads(95) Cited by(0)

On the geometric dependence of Riemannian Sobolev best constants

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

On the geometric dependence of Riemannian Sobolev best constants

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content