The topic of my Master’s thesis, “Divergence-measure fields: generalizations of Gauss-Green formula with applications“, which I wrote under the supervision of Prof. K. R. Payne, concerns the study of$L^p$-summable vector fields whose divergence is a Radon measure, in order to achieve a generalization of the classical divergence theorem in the context of sets of finite perimeter.
These fields were introduced some years ago in order to study nonlinear hyperbolic systems of conservation laws by Chen and Frid, and also the fundaments of continuum mechanics by Degiovanni, Marzocchi, Musesti and Šilhavý.
We explored especially the case $p=\infty$.
The method of the proof of the Gauss-Green formula for essentially bounded
divergence-measure fields is however different from the previous ones, since we adapted the techniques already developed for BV functions in Vol’pert’s work.http://cvgmt.sns.it/seminar/513/
