The Gauss-Green theorem (Q5903995)

This is a summary of recent contribution of the author to the Gauss-Green formula, namely the set of assumptions under which the classical formula \[ \int_{A}div v=\int_{\partial A}v\cdot n_ A \] holds. Because of the increase in technicality required to be able to integrate more singular fields on more general sets, with respect to pioneering work of the reviewer, Jarnik, Kurzweil, Schwabik, Pfeffer in this direction, the author has put emphasis, in this survey, on the basic underlying ideas and philosophy and he concludes by insisting upon the need of an axiomatic characterization in order to help the choice among the various averaging methods presently available.