Selected Publications:

  1. Lagrangian Dynamics on an infinite-dimensional torus; a Weak KAM theorem. (A. Tudorascu). To Appear in Advances in Mathematics.
  2. Differential forms on Wasserstein space and infinite dimensional Hamiltonian systems. (H.K. Kim, T. Pacini). To appear in Memoirs of AMS.
  3. Optimal transport for the system of isentropic Euler equations. (M. Westdickenberg), To appear in Comm. PDEs.
  4. Hamilton-Jacobi equations in the Wasserstein space. (T. Nguyen, A. Tudorascu), Meth. Appl. Anal. Vol. 15 no 2, 155--184, 2008.
  5. Michell Trusses and Lines of Principal Actions. (G. Bouchitte and P. Seppecher), Math. Models Meth. Applied Sci. Vol. 18, 9,1571--1603, 2008.
  6. Euler-Poisson systems as action-minimizing paths in the Wasserstein space. (T. Nguyen, A. Tudorascu), Arch. Rat. Mech. Analysis, 2008.
  7. Hamiltonian ODE's in the Wasserstein space of probability measures. (L. Ambrosio). Comm. Pure Applied Math., Vol. LXI, 0018--0053, 2008.
  8. The Semigeostrophic Equations Discretized in reference and dual variables. (M. Cullen and G. Pisante). Arch. Rat. Mech. Analysis 185, no 2, 341--363, 2007.
  9. Existence of Optimal Maps in the Reflector-type Problems. (V. Oliker). COCV, ESAIM 13, no 1, 93--106, 2007.
  10. Extension Theorems for Vector Valued Maps. (B. Dacorogna). Jour. Math Pure Appliquees (9), 85, no. 3, 313--344, 2006.
  11. On some nonlocal variational problems. (M. Chipot and B. Kawohl). Anal. Appl. (Singap.) 4, no. 4, 345-356, 2006.
  12. Diffeomorphisms and Nonlinear Heat Flows. (L.C. Evans and O. Savin). SIAM Math Ana., 37, no. 3, 737--751 (electronic) 2005.
  13. On the solution of a model Boltzmann equation via constrained steepest ascent in a Wasserstein metric. (E. Carlen). Arch. Rational Mech. Ana., 172, no. 1, 21--64, 2004.
  14. Inequalities for generalized entropy and optimal transportation. (D. Cordero and C. Houdré). Comteporary Mathematics, AMS Vol 353, 2004.
  15. Constrained Steepest Descent in the 2--Wasserstein Metric. (E. Carlen). Annals of Mathematics. Vol 157, 3, 2003.
  16. L^p -Approximation of maps by diffeomorphisms. (Y. Brenier) Cal. Variations and PDE, 16 (2003), no. 2, 147--164.
  17. A Variational Approach for the 2-D Semi-Geostrophic Shallow Water Equations. (M. Cullen) Arch. Rat. Mech. and Anal., 2001.
  18. Uniqueness of Equilibrium Configurations in Solid Crystals. (R. Van der Putten) SIAM Math. Anal. no 3, 465--492, 2000.
  19. Shape Recognition via Wasserstein Distance. (R. McCann) Quarterly Appl. Math., no 4, 705--737, 2000.
  20. Geometric Restrictions for the Existence of Viscosity Solutions. (P. Cardarliaguet et al.) Ann. Inst. Henri Poincare, 189--220, 1999.
  21. Differential Methods for the the Monge-Kantorovich Mass Transfer Problems. (L.C. Evans) Memoirs of AMS., no 653, vol. 137, 1999.
  22. The Monge Mass Transfer Problems and Its Applications. NSF-CBMS Conference. Contemporary Mathematics, Vol 226 (1999).
  23. Optimal Maps for the Multidimensional Monge-Kantorovich Problem. (A. Swiech) Commu. Pure Applied Math., 23--45, 1998.
  24. The geometry of optimal transport. (R. McCann) Acta Mathematica, Vol 177, 113--161, 1996.
  25. An elementary proof of the polar decomposition of vector-valued functions. Arch. Rat. Mech. Anal., Vol. 128, 380-399, 1995.

Preprints:

  1. A variational method for class of parabolic PDEs. (A. Figalli, T. Yolcu)

Lecture Notes:

  1. Carnegie Mellon 2004 Summer Institute .
  2. Habilitations (1995): Xerox copy of the section on the Monge-Kantorovich theory. (W. Gangbo).

Book reviewed:

  1. Review on the book "Gradient flows in metric spaces and in the space of probability measures" by Ambrosio, Gigli and Savare.
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