Multi-material transport problems

In this joint works with Andrea Marchese and co-authors, we propose an Eulerian formulation for the multicommodity flow problem, i.e. a general branched transportation problem in which m different goods are moved simultaneously. Moreover, in the atomic case, we prove that the problem can be relaxed in a mass minimization problem in a class of rectifiable currents with coefficients in a group, allowing to introduce a notion of calibration. Finally, I will show how these tools allow the modelling of the oriented mailing problem.