Hardy inequalities on Riemannian manifolds and applications

被引：68

作者：

D'Ambrosio, Lorenzo ^{[1
]}

Dipierro, Serena ^{[2
]}

机构：

[1] Dipartimento Matemat, I-70125 Bari, Italy

[2] SISSA, Sect Math Anal, I-34136 Trieste, Italy

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2014年 / 31卷 / 03期

关键词：

Hardy inequality; Riemannian manifolds; Parabolic manifolds; Caccioppoli inequality; Weighted Gagliardo-Nirenberg inequality; Interpolation inequality; GAGLIARDO-NIRENBERG INEQUALITIES; RELLICH INEQUALITIES; P-LAPLACIAN; CONSTANTS;

D O I：

10.1016/j.anihpc.2013.04.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a simple sufficient criterion to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second order differential operator Delta(p)u := diva (vertical bar del u vertical bar(P-2) del u). Namely, if p is a nonnegative weight such that -Delta(p)p >= 0, then the Hardy inequality [GRAPHICS] holds. We show concrete examples specializing the function p. Our approach allows to obtain a characterization of p-hyperbolic manifolds as well as other inequalities related to Caccioppoli inequalities, weighted Gagliardo-Nirenberg inequalities, uncertain principle and first order Caffarelli-Kohn-Nirenberg interpolation inequality. (C) 2013 Elsevier Masson SAS. All rights reserved.

引用

页码：449 / 475

页数：27

共 50 条

[1]

Adimurthi, 2006, P ROY SOC EDINB A, V136, P1111

[2] Hardy type inequalities on complete Riemannian manifolds [J].