Limiting Sobolev and Hardy inequalities on stratified homogeneous groups
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
AbstractWe 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.
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
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