Limiting Sobolev and Hardy inequalities on stratified homogeneous groups

Authors

  • Jean Van Schaftingen Université catholique de Louvain, Institut de Recherche en Mathématique et Physique (IRMP)
  • Po-Lam Yung The Chinese University of Hong Kong, Department of Mathematics, and Australian National University, Mathematical Sciences Institute

DOI:

https://doi.org/10.54330/afm.120959

Keywords:

Sobolev embedding, overdetermined elliptic operator, compatibility conditions, homogeneous differential operator, maximally hypoelliptic operator, canceling operator, cocanceling operator, exterior derivative, symmetric derivative, Korn-Sobolev inequality, Hodge inequality, Saint-Venant compatibility conditions

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.

 

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Published

2022-08-16

Issue

Vol. 47 No. 2 (2022)

Section

Articles

License

Copyright (c) 2022 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Van Schaftingen, J., & Yung, P.-L. (2022). Limiting Sobolev and Hardy inequalities on stratified homogeneous groups. Annales Fennici Mathematici, 47(2), 1065-1098. https://doi.org/10.54330/afm.120959