Free access
Issue
ESAIM: M2AN
Volume 41, Number 6, November-December 2007
Page(s) 1041 - 1060
DOI http://dx.doi.org/10.1051/m2an:2007051
Published online 15 December 2007
  1. L. Ambrosio, Optimal transport maps in Monge-Kantorovich problem, Proceedings of the ICM (Beijing, 2002) III. Higher Ed. Press, Beijing (2002) 131–140.
  2. L. Ambrosio, Lecture notes on optimal transport, in Mathematical Aspects of Evolving Interfaces, L. Ambrosio et al. Eds., Lect. Notes in Math. 1812 (2003) 1–52.
  3. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Clarendon Press, Oxford (2000).
  4. S. Angenent, S. Haker and A. Tannenbaum, Minimizing flows for the Monge-Kantorovich problem. SIAM J. Math. Anal. 35 (2003) 61–97. [CrossRef] [MathSciNet]
  5. G. Aronson, L.C. Evans and Y. Wu, Fast/slow diffusion and growing sandpiles. J. Diff. Eqns. 131 (1996) 304–335. [CrossRef]
  6. C. Bahriawati and C. Carstensen, Three Matlab implementations of the lowest-order Raviart-Thomas MFEM with a posteriori error control. Comput. Methods Appl. Math. 5 (2005) 333–361. [CrossRef] [MathSciNet]
  7. J.W. Barrett and L. Prigozhin, Dual formulations in critical state problems. Interfaces Free Boundaries 8 (2006) 347–368.
  8. J.W. Barrett and L. Prigozhin, Partial L1 Monge-Kantorovich problem: variational formulation and numerical approximation. (Submitted).
  9. J.-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375–393. [CrossRef] [MathSciNet]
  10. G. Bouchitté, G. Buttazzo and P. Seppecher, Shape optimization solutions via Monge-Kantorovich equation. C.R. Acad. Sci. Paris 324-I (1997) 1185–1191.
  11. L.A. Caffarelli and R.J. McCann, Free boundaries in optimal transport and Monge-Ampère obstacle problems. Ann. Math. (to appear).
  12. R. De Arcangelis and E. Zappale, The relaxation of some classes of variational integrals with pointwise continuous-type gradient constraints. Appl. Math. Optim. 51 (2005) 251–277. [CrossRef] [MathSciNet]
  13. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976).
  14. L.C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations, C.B.M.S. 74. AMS, Providence RI (1990).
  15. L.C. Evans, Partial differential equations and Monge-Kantorovich mass transfer, Current Developments in Mathematics. Int. Press, Boston (1997) 65–126.
  16. L.C. Evans and W. Gangbo, Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem. Mem. Amer. Math. Soc. 137 (1999).
  17. M. Farhloul, A mixed finite element method for a nonlinear Dirichlet problem. IMA J. Numer. Anal. 18 (1998) 121–132. [CrossRef] [MathSciNet]
  18. M. Farhloul and H. Manouzi, On a mixed finite element method for the p-Laplacian. Can. Appl. Math. Q. 8 (2000) 67–78. [CrossRef]
  19. M. Feldman, Growth of a sandpile around an obstacle, in Monge Ampere Equation: Applications to Geometry and Optimization, L.A Caffarelli and M. Milman Eds., Contemp. Math. 226, AMS, Providence (1999) 55–78.
  20. G.B. Folland, Real Analysis: Modern Techniques and their Applications (Second Edition). Wiley-Interscience, New York (1984).
  21. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, Berlin (1986).
  22. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman, Massachusetts (1985).
  23. A. Pratelli, Equivalence between some definitions for the optimal mass transport problem and for transport density on manifolds. Ann. Mat. Pura Appl. 184 (2005) 215–238. [CrossRef] [MathSciNet]
  24. L. Prigozhin, Variational model for sandpile growth. Eur. J. Appl. Math. 7 (1996) 225–235.
  25. L. Prigozhin, Solutions to Monge-Kantorovich equations as stationary points of a dynamical system. arXiv:math.OC/0507330, http://xxx.tau.ac.il/abs/math.OC/ 0507330 (2005).
  26. L. Rüschendorf and L. Uckelmann, Numerical and analytical results for the transportation problem of Monge-Kantorovich. Metrika 51 (2000) 245–258. [CrossRef] [MathSciNet]
  27. G. Strang, L1 and L approximation of vector fields in the plane. Lecture Notes in Num. Appl. Anal. 5 (1982) 273–288.
  28. C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics 58. AMS, Providence RI (2003).

Recommended for you