Limiting Sobolev and Hardy inequalities on stratified homogeneous groups
Jean Van Schaftingen, Po-Lam Yung

TL;DR
This paper establishes conditions under which limiting Sobolev and Hardy inequalities hold on stratified homogeneous groups, extending known Euclidean results to a broader geometric setting, and deriving endpoint Korn inequalities.
Contribution
It provides a sufficient condition for limiting inequalities on stratified groups, generalizing Euclidean cancelling conditions and deriving endpoint Korn inequalities.
Findings
Sufficient condition for limiting Sobolev and Hardy inequalities on stratified groups
Extension of Euclidean cancelling condition to stratified homogeneous groups
Derivation of endpoint Korn--Sobolev and Korn--Hardy inequalities
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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Taxonomy
TopicsNonlinear Partial Differential Equations
