CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Abstract
Aim of this paper is to show that it makes sense to write the continuity equation on a metric measure space (X,d,m) and that absolutely continuous curves (\mu_t) w.r.t. the distance W_2 can be completely characterized as solutions of the continuity equation itself, provided we impose the condition μ_t ≤ Cm for every t and some C > 0.
