Resumen de Subelliptic Bourgain--Brezis estimates on groups

Sagun Chanillo, Jean van Schaftingen

• We show that divergence-free $\mathrm{L}^1$ vector fields on a nilpotent homogeneous group of homogeneous dimension $Q$ are in the dual space of functions whose gradient is in $\mathrm{L}^Q$. This was previously obtained on $\R^n$ by Bourgain and Brezis.