Dedicated to Vladimir Maz'ya on the occasion of his 70th birthday, with high esteem and friendship Abstract. We study various questions related to the best constants in the
We show that divergence-free L 1 vector fields on a nilpotent homogeneous group of homogeneous dimension Q are in the dual space of functions whose gradient is in L Q. This was previously obtained on R n by Bourgain and Brezis.
We obtain boundary estimates for the gradient of solutions to elliptic systems with Dirichlet or Neumann boundary conditions and L 1 –data, under some condition on the divergence of the data. Similar boundary estimates are obtained for div–curl and Hodge systems.