On the lack of compactness on stratified Lie groups

Abstract

In $\mathbb{R}^d$, the characterization of the \mbox{lack of compactness of the continuous Sobolev injection $\mathring{H}^s \hookrightarrow L^p$}, with $\displaystyle{\frac{s}{d} + \frac{1}{p} = \frac{1}{2}}$ and $\displaystyle{