Gradient flows in Wasserstein spaces and applications to crowd movement
Starting from a motivation in the modeling of crowd movement, the paper presents the topics of gradient flows, first in , then in metric spaces, and finally in the space of probability measures endowed with the Wasserstein distance (induced by the quadratic transport cost). Differently from the usual theory by Jordan-Kinderlehrer-Otto and Ambrosio-Gigli-Savaré, we propose an approach where the optimality conditions for the minimizers of the optimization problems that one solves at every time step...