  We prove a Pontryagin Maximum Principle for optimal control problems in the
space of probability measures, where the dynamics is given by a transport
equation with non-local velocity. We formulate this first-order optimality
condition using the formalism of subdifferential calculus in Wasserstein
spaces. We show that the geometric approach based on needle variations and on
the evolution of the covector (here replaced by the evolution of a mesure on
the dual space) can be translated into this formalism.
