Optimal Transport References

From PDEwiki

• Books, Lecture Notes, and Survey articles
  • Cedric Villani. Topics in Optimal Transportation. American Mathematical Society, Graduate Studies in Mathematics series, vol. 58 (2003).
  • Cedric Villani. St. Flour Lecture Notes on Optimal Transportation (in progress).
  • Luigi Ambrosio Lecture Notes on Optimal Transport Problems (2000)
  • Lawrence Evans. Partial Differential Equations and Monge-Kantorovich Mass Transfer Prepritn. 2001.

• Basic Theory
  • Robert McCann. Existence and uniqueness of monotone measure-preserving maps. Duke Math. J. 80, 309-323, (1995)
  • Wilfrid Gangbo and Robert McCann. Optimal maps in Monge's mass transport problem C.R. Acad. Sci. Paris. Ser. I. Math. 325, 1653-1658 (1995)
  • Wilfrid Gangbo and Robert McCann. The geometry of optimal transportation. Acta Math. 177, 113-161 (1996)

• Free boundary problems
  • Luis A. Caffarelli and Robert McCann. Free boundaries in optimal transport and Monge-Ampere obstacle problems. Preprint 2005.

• Regularity theory
  • X.Ma, N.Trudinger, and X.-J. Wang. Regularity of potential functions of the optimal transportation problem. Arch. Rat. Mech. Anal., 177(2005), 151-183.
  • Neil Trudinger and Xu-Jia Wang. On the second boundary value problem for Monge Ampere type equations and optimal transportation Preprint.
  • Grégoire Loeper. Continuity of maps solutions of optimal transportation problems. preprint.

• Nonlinear evolutions
  • Felix Otto. The geometry of dissipative evolution equations: the porous medium equation. Comm. Partial Differential Equations, 26(1-2):101-174, 2001.

• Hamiltonian Aspects
  • Luigi Ambrosio and Wilfrid Gangbo. Hamiltonian ODE's in the Wasserstein space of probability measures (2005)

• Other Applications
  • Wilfrid Gangbo and Robert McCann. Shape Recognition via Wasserstein Distance. Quarterly Appl. Math., no 4, 705--737, 2000.

• Useful Links

Luigi Ambrosio Lawrence Evans Wilfrid Gangbo Robert McCann Felix Otto Neil Trudinger Cedric Villani Xu-Jia Wang