In this note we prove that, if the cost function satisfies some necessary structural conditions and the densities are bounded away from zero and infinity, then strictly c-convex potentials arising in optimal transportation belong to W2,1+κloc for some κ>0. This generalizes some recents results concerning the regularity of strictly convex Alexandrov solutions of the Monge-Amp\`ere equation with right hand side bounded away from zero and infinity.
