Selected Publications:

  1. On the matrix Monge-Kantorovich problem. (Y. Chen, T.T. Georgiou, A. Tannenbaum). To appear in Euro J. Applied Math
  2. A partial Laplacian as an infinitesimal generator on the Wasserstein space. (Y.T.~chow). To appear in JDE.
  3. Geodesic of minimal length in the set of probability measures on graphs (W. Li, C. Mou). To appear in ESAIM: COCV
  4. Quasiconvexity and Relaxation in Optimal Transportation of Closed Differential Forms. (B. Dacorogna). To appear in Arch. Rat. Mech. Analysis.
  5. On differentiability in the Wasserstein space and well-posedness for Hamilton-Jacobi equations. (A. Tudorascu). J. Math Pures Appl., Vol 125, 119--174, 2018.
  6. Transportation of differential forms with non-homogeneous convex costs. (B. Dacorogna). Cal. Var. and PDEs 57, no 4, 2018.
  7. Symplectic decomposition, Darboux theorem and ellipticity. (B. Dacorogna, O. Kneuss). Annales de l'Institut Henri--Poincar\'e C, Analyse non lineaire, vol. 35, 327--356, 2018.
  8. A fast algorithm for earth mover's distance based on optimal transport and L1 type regularization. (W. Li, E. Ryu, S. Osher, W. Yin). Journal of Scientific Computing, vol. 75, issue 1, 182--192, 2018.
  9. An optimal transport approach for the kinetic Bohmian Equation. (J.~Haskovec, P.~ Markowich and J.~Sierra). Zapiski Nauchnyh Seminarov POMI, vol. 457, 114--167, 2017.
  10. Optimal transport of closed differential forms for convex costs. (B. Dacorogna, O. Kneuss). Comptes Rendus des Acad\'emies de Sciences, Volume 353, Issue 12, 1099--1104, 2015.
  11. Existence of a solution to an equation arising from Mean Field Games. (A. Swiech). J. Differential Equations 259, no. 11, 6573--6643, 2015.
  12. A mathematically rigorous analysis of forced axisymmetric flows in the atmosphere. (M. Cullen and M. Sedjro) Quarterly Journal of the Royal Meteorological Society, 141, issue 690, 1836 -- 1844, 2015.
  13. Metric Viscosity Solutions of Hamilton-Jacobi Equations Depending on Local Slopes. (A. Swiech). Calculus of Variations and Partial Differential Equations, 54, no 1, 1183 -- 1218, 2015.
  14. A Polyconvex Integrand; Euler-Lagrange Equations and Uniqueness of equilibrium. (R. Awi) Arch. Rat. Mech. Anal. 214, no 1, 143 -- 182, 2014.
  15. Optimal Transport and Large Number of Particles. (A. Swiech). Discret. Cont. Dynam. Syst.-- A 34 1397 -- 1441, 2014
  16. Weak KAM Theory on the Wasserstein Torus with Multidimensional Underlying Space. (A. Tudorascu). Comm. Pures Appl. Math., Volume 67, Issue 3, 408 -- 463, 2014.
  17. Sticky particle dynamics with interactions. (Y. Brenier, G. Savare and M. Westdickenberg). Journal de Math. Pures et Appl., no 99, 577--617, 2013.
  18. Hamiltonian ODE's on a Space of Deficient Measures. (L. Chayes and H. Lei). Communications in Mathematical Sciences, 11, no. 1, 1--31, 2013.
  19. Homogenization for a class of integral functionals in spaces of probability measures. (A. Tudorascu). Adv. Math., Vol 230, issue 3, 1124--1173, 2012.
  20. A variational method for class of parabolic PDEs. (A. Figalli, T. Yolcu). Annali Scuola N. Pisa, Cl. Sci. (5), 10, no. 1, 207--252, 2011
  21. Differential forms on Wasserstein space and infinite dimensional Hamiltonian systems. (H.K. Kim, T. Pacini). Memoirs of AMS, Vol 211, no 993, 2011.
  22. A Weak KAM theorem; from finite to infinite dimenson. (A. Tudorascu). Edizioni della Normale, 2010.
  23. Lagrangian Dynamics on an infinite-dimensional torus; a Weak KAM theorem. (A. Tudorascu). Adv. Math. 224, no. 1, 260--292, 2010.
  24. Optimal transport for the system of isentropic Euler equations. (M. Westdickenberg), Comm. PDEs 34, no. 7-9, 1041--1073, 2009.
  25. Hamilton-Jacobi equations in the Wasserstein space. (T. Nguyen, A. Tudorascu), Meth. Appl. Anal. Vol. 15 no 2, 155--184, 2008.
  26. Michell Trusses and Lines of Principal Actions. (G. Bouchitte and P. Seppecher), Math. Models Meth. Applied Sci. Vol. 18, 9,1571--1603, 2008.
  27. Euler-Poisson systems as action-minimizing paths in the Wasserstein space. (T. Nguyen, A. Tudorascu), Arch. Rat. Mech. Analysis, 2008.
  28. Hamiltonian ODE's in the Wasserstein space of probability measures. (L. Ambrosio). Comm. Pure Applied Math., Vol. LXI, 0018--0053, 2008.
  29. The Semigeostrophic Equations Discretized in reference and dual variables. (M. Cullen and G. Pisante). Arch. Rat. Mech. Analysis 185, no 2, 341--363, 2007.
  30. Existence of Optimal Maps in the Reflector-type Problems. (V. Oliker). COCV, ESAIM 13, no 1, 93--106, 2007.
  31. Extension Theorems for Vector Valued Maps. (B. Dacorogna). Jour. Math Pure Appliquees (9), 85, no. 3, 313--344, 2006.
  32. On some nonlocal variational problems. (M. Chipot and B. Kawohl). Anal. Appl. (Singap.) 4, no. 4, 345-356, 2006.
  33. Diffeomorphisms and Nonlinear Heat Flows. (L.C. Evans and O. Savin). SIAM Math Ana., 37, no. 3, 737--751 (electronic) 2005.
  34. 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.
  35. Inequalities for generalized entropy and optimal transportation. (D. Cordero and C. Houdré). Comteporary Mathematics, AMS Vol 353, 2004.
  36. Constrained Steepest Descent in the 2--Wasserstein Metric. (E. Carlen). Annals of Mathematics. Vol 157, 3, 2003.
  37. L^p -Approximation of maps by diffeomorphisms. (Y. Brenier) Cal. Variations and PDE, 16 (2003), no. 2, 147--164.
  38. A Variational Approach for the 2-D Semi-Geostrophic Shallow Water Equations. (M. Cullen) Arch. Rat. Mech. and Anal., 2001.
  39. Uniqueness of Equilibrium Configurations in Solid Crystals. (R. Van der Putten) SIAM Math. Anal. no 3, 465--492, 2000.
  40. Shape Recognition via Wasserstein Distance. (R. McCann) Quarterly Appl. Math., no 4, 705--737, 2000.
  41. Geometric Restrictions for the Existence of Viscosity Solutions. (P. Cardarliaguet et al.) Ann. Inst. Henri Poincare, 189--220, 1999.
  42. Differential Methods for the the Monge-Kantorovich Mass Transfer Problems. (L.C. Evans) Memoirs of AMS., no 653, vol. 137, 1999.
  43. The Monge Mass Transfer Problems and Its Applications. NSF-CBMS Conference. Contemporary Mathematics, Vol 226 (1999).
  44. Optimal Maps for the Multidimensional Monge-Kantorovich Problem. (A. Swiech) Commu. Pure Applied Math., 23--45, 1998.
  45. The geometry of optimal transport. (R. McCann) Acta Mathematica, Vol 177, 113--161, 1996.
  46. An elementary proof of the polar decomposition of vector-valued functions. Arch. Rat. Mech. Anal., Vol. 128, 380-399, 1995.
  47. Local invertibility of Sobolev functions. (I.Fonseca) SIAM Journal of Math. Ana., Vol. 26, no. 2, 280--304, 1995.
  48. On the weak lower semi-continuity of a polyconvex integrand. Journal de Mathematiques Pures et Appliquees, Vol. 73, no. 5, 455-469, 1994.
  49. On the envelopes of functions depending on singular values of matrices. (G. Buttazzo, B. Dacorogna) Bollettino, U.M.I. (7)8-B, 17-35, 1994.
  50. On the continuity of the polyconvex, quasiconvex and rank one convex envelope with respect to the growth condition. Proceed. of the Royal Society of Edinburgh, 123A, 707-729, 1993.
  51. Sur une generalisation de l'inegalite de Wirtinger. (B. Dacorogna, N. Subia) Annales de l'Institut Henri Poincar\'{e}, Analyse non Lineaire (Paris), Vol.9, 29-50, 1992.
  52. Some examples of rank one convex functions in dimension two. (B. Dacorogna, J. Douchet, J. Rappaz) Proceed. of the Royal Society of Edinburgh, 114A, 135-150, 1990.


  1. Unnormalized optimal transport. (W.~L, S.~Osher and M.~Puthawala).
  2. Lecture Notes:

    1. Carnegie Mellon 2004 Summer Institute .
    2. Habilitations (1995): Xerox copy of the section on the Monge-Kantorovich theory. (W. Gangbo).
    3. Discrete Decomposition of Discrete Forces (posted Feb 2011). (W. Gangbo).
    4. On some analytical aspects of Mean Field Games (posted April 2019). Lecture Notes based on a class taught in Berkeley during Fall 2018 (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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