On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and p-sub-Laplacian inequalities on stratified groups

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Ruzhansky, Michael¹  Suragan, Durvudkhan^1,2 

[1] Imperial Coll London, Dept Math, 180 Queens Gate, London SW7 2AZ, England

[2] Inst Math & Math Modelling, 125 Pushkin Str, Alma Ata 050010, Kazakhstan

关键词: Hardy inequality;    Rellich inequality;    Caffarelli-Kohn-Nirenberg inequality;    p-sub-Laplacian;    Horizontal estimate;    Stratified group;   

DOI  :  10.1016/j.jde.2016.10.028

来源: Elsevier

【 摘 要 】

In this paper, we present a version of horizontal weighted Hardy-Rellich type and Caffarelli-Kohn-Nirenberg type inequalities on stratified groups and study some of their consequences. Our results reflect on many results previously known in special cases. Moreover, a new simple proof of the Badiale-Tarantello conjecture [2] on the best constant of a Hardy type inequality is provided. We also show a family of Poincard inequalities as well as inequalities involving the weighted and unweighted p-sub-Laplacians. (C) 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license.

【 授权许可】

Free