Limiting Sobolev and Hardy inequalities on stratified homogeneous groups

Kirjoittajat

  • 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

Avainsanat:

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

Abstrakti

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.

 

Tiedostolataukset

Julkaistu

2022-08-16

Numero

Vol 47 Nro 2 (2022)

Osasto

Articles

Lisenssi

Copyright (c) 2022 Annales Fennici Mathematici

Creative Commons License

Tämä työ on lisensoitu Creative Commons Nimeä-EiKaupallinen 4.0 Kansainvälinen Julkinen -lisenssillä.

Viittaaminen

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