The study of divergence‐measure fields has significantly advanced the analytical framework underpinning classical Gauss–Green theorems by extending their applicability to irregular settings.

In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector fields that can have singularities at every point of a compact set whose Minkowski content of codimension ...

We propose a new numerical approach for two-dimensional Maxwell's equations that is based on the Hodge decomposition for divergence-free vector fields. In this approach an approximate solution for ...