On the distributional normal trace

This talk concerns the validity of the Gauss-Green formula when the underlying field is highly irregular, in the sense of being measure-valued. This can be understood by replacing the boundary integral by distributional pairing, giving rise to the so-called normal trace, which need not be a measure in general. Working in the framework of divergence-measure fields, we will obtain a sharp identification of the space of such normal traces, and as an application we will establish extension results for divergence-measure and divergence-free fields.