Some new linear L1-estimates

The aim of this talk is to review recent advances building on the fundamental work of Bourgain, Brezis, Mironescu, and Van Schaftingen in the study of linear (elliptic) systems $B u=f$, where the source term is a Radon measure. The results discussed will cover aspects of critical Sobolev regularity, boundary estimates, and fine properties of the solutions. Special attention will be given to the case of operators of order $n$ on $R^n$, in which case the operators $B$ for which the solution $u$ is bounded or continuous are characterized.