ABSTRACT
For bounded vector fields, and then for continuous vector fields, we characterize distributions which are their distributional divergences. These results, obtained jointly by T. De Pauw and the author [23], extend parts of an earlier work of J. Bourgain and H. Brezis [10]. As the proofs involve functional analysis in an essential way, some familiarity with basic properties of locally convex spaces is assumed. More specialized facts are presented with precise references, but often without proofs.
