Sharp k-order Sobolev inequalities in the hyperbolic space \Bbb Hⁿ

2007/08/02 by Genqian Liu, Liu, Genqian
Engineering · Mathematics · #35J35 #35J60 #46E35 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0708.0269

openalex publication_date 2007/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain the sharp k-th order Sobolev inequalities in the hyperbolic space \Hⁿ for all k=1,2,3,⋯. This gives an answer to an open question raised by Aubin in [5, p. 176-177] for W^k,2(\Hⁿ) with k>1. In addition, we prove that the associated Sobolev constants are optimal.

Citations

• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation

Related

• Optimal Sobolev inequalities in the hyperbolic space
• The sharp Poincaré--Sobolev type inequalities in the hyperbolic spaces \mathbb Hⁿ
• Second order Sobolev type inequalities in the hyperbolic spaces
• The sharp higher order Lorentz--Poincar 'e and Lorentz--Sobolev\n inequalities in the hyperbolic spaces
• The sharp Sobolev type inequalities in the Lorentz--Sobolev spaces in\n the hyperbolic spaces