Geodesic
Limiting Sobolev and Hardy inequalities on stratified homogeneous groups
Jean Van Schaftingen1 ; Po-Lam Yung2
1Université catholique de Louvain, Institut de Recherche en Mathématique et Physique (IRMP)
2The Chinese University of Hong Kong, Department of Mathematics, and Australian National University, Mathematical Sciences Institute
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 1065-1098

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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.  
DOI : 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

Jean Van Schaftingen  1   ; Po-Lam Yung  2

1 Université catholique de Louvain, Institut de Recherche en Mathématique et Physique (IRMP)
2 The Chinese University of Hong Kong, Department of Mathematics, and Australian National University, Mathematical Sciences Institute 
Jean Van Schaftingen; Po-Lam Yung. Limiting Sobolev and Hardy inequalities on stratified  homogeneous groups. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 1065-1098. doi: 10.54330/afm.120959
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