Limiting Sobolev and Hardy inequalities on stratified homogeneous groups

Jean Van Schaftingen; Po Lam Yung

doi:10.54330/AFM.120959

Limiting Sobolev and Hardy inequalities on stratified homogeneous groups

Jean Van Schaftingen^*, Po Lam Yung

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We give a sufficient condition for limiting Sobolev and Hardy inequalities to hold on stratified homogeneous groups. In the Euclidean case, this condition reduces to the known cancelling necessary and sufficient condition. We obtain in particular endpoint Korn–Sobolev and Korn–Hardy inequalities on stratified homogeneous groups.

Original language	English
Pages (from-to)	1065-1098
Number of pages	34
Journal	Annales Fennici Mathematici
Volume	47
Issue number	2
DOIs	https://doi.org/10.54330/AFM.120959
Publication status	Published - 2022

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title = "Limiting Sobolev and Hardy inequalities on stratified homogeneous groups",

abstract = "We give a sufficient condition for limiting Sobolev and Hardy inequalities to hold on stratified homogeneous groups. In the Euclidean case, this condition reduces to the known cancelling necessary and sufficient condition. We obtain in particular endpoint Korn–Sobolev and Korn–Hardy inequalities on stratified homogeneous groups.",

keywords = "Canceling operator, Cocanceling operator, Compatibility conditions, Exterior derivative, Hodge inequality, Homogeneous differential operator, Korn–sobolev inequality, Maximally hypoelliptic operator, Overdetermined elliptic operator, Saint-venant compatibility conditions, Sobolev embedding, Symmetric derivative",

author = "Schaftingen, \{Jean Van\} and Yung, \{Po Lam\}",

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T1 - Limiting Sobolev and Hardy inequalities on stratified homogeneous groups

AU - Schaftingen, Jean Van

AU - Yung, Po Lam

PY - 2022

Y1 - 2022

N2 - We give a sufficient condition for limiting Sobolev and Hardy inequalities to hold on stratified homogeneous groups. In the Euclidean case, this condition reduces to the known cancelling necessary and sufficient condition. We obtain in particular endpoint Korn–Sobolev and Korn–Hardy inequalities on stratified homogeneous groups.

AB - We give a sufficient condition for limiting Sobolev and Hardy inequalities to hold on stratified homogeneous groups. In the Euclidean case, this condition reduces to the known cancelling necessary and sufficient condition. We obtain in particular endpoint Korn–Sobolev and Korn–Hardy inequalities on stratified homogeneous groups.

KW - Canceling operator

KW - Cocanceling operator

KW - Compatibility conditions

KW - Exterior derivative

KW - Hodge inequality

KW - Homogeneous differential operator

KW - Korn–sobolev inequality

KW - Maximally hypoelliptic operator

KW - Overdetermined elliptic operator

KW - Saint-venant compatibility conditions

KW - Sobolev embedding

KW - Symmetric derivative

UR - https://www.scopus.com/pages/publications/85138039953

U2 - 10.54330/AFM.120959

DO - 10.54330/AFM.120959

M3 - Article

SN - 2737-0690

VL - 47

SP - 1065

EP - 1098

JO - Annales Fennici Mathematici

JF - Annales Fennici Mathematici

IS - 2

ER -

Limiting Sobolev and Hardy inequalities on stratified homogeneous groups

Abstract

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