Optimal regions for congested transport.

Summary We consider a given region Ω where the traffic flows according to two regimes: in a region C we have a low congestion, where in the remaining part Ω∖C the congestion is higher. The two congestion functions H1 and H2 are given, but the region C has to be determined in an optimal way in order to minimize the total transportation cost. Various penalization terms on C are considered and some numerical computations are shown.