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

Michael Ruzhansky; Durvudkhan Suragan

doi:10.1016/j.jde.2016.10.028

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

Michael Ruzhansky, Durvudkhan Suragan

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

64 Citations (Scopus)

Abstract

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 Poincaré inequalities as well as inequalities involving the weighted and unweighted p-sub-Laplacians.

Original language	English
Pages (from-to)	1799-1821
Number of pages	23
Journal	Journal of Differential Equations
Volume	262
Issue number	3
DOIs	https://doi.org/10.1016/j.jde.2016.10.028
Publication status	Published - Feb 5 2017

Keywords

Caffarelli–Kohn–Nirenberg inequality
Hardy inequality
Horizontal estimate
p-sub-Laplacian
Rellich inequality
Stratified group

ASJC Scopus subject areas

Analysis

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10.1016/j.jde.2016.10.028

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

abstract = "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 Poincar{\'e} inequalities as well as inequalities involving the weighted and unweighted p-sub-Laplacians.",

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AU - Suragan, Durvudkhan

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Y1 - 2017/2/5

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AB - 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 Poincaré inequalities as well as inequalities involving the weighted and unweighted p-sub-Laplacians.

KW - Caffarelli–Kohn–Nirenberg inequality

KW - Hardy inequality

KW - Horizontal estimate

KW - p-sub-Laplacian

KW - Rellich inequality

KW - Stratified group

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

Abstract

Keywords

ASJC Scopus subject areas

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