A parabolic flow toward solutions of the optimal transportation problem on domains with boundary
arXiv:1007.4526
Abstract
We consider a parabolic version of the mass transport problem, and show that it converges to a solution of the original mass transport problem under suitable conditions on the cost function, and initial and target domains.
32 pages, minor typos fixed, "strictly c-convex" changed to "locally, uniformly c-convex." To appear in J. Reine Angew. Math