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All issues Volume 49 / No 6 (November-December 2015) ESAIM: M2AN, 49 6 (2015) 1643-1657 References
Issue
ESAIM: M2AN
Volume 49, Number 6, November-December 2015
Special Issue - Optimal Transport
Page(s) 1643 - 1657
DOI https://doi.org/10.1051/m2an/2015035
Published online 05 November 2015
  1. M. Beiglböck, Ch. Léonard and W. Schachermayer, A general duality theorem for the monge–kantorovich transport problem. Stud. Math. 209 (2012) 2. [Google Scholar]
  2. A. Braides, Gamma-convergence for Beginners. Vol. 22. Oxford University Press, Oxford (2002). [Google Scholar]
  3. G. Buttazzo, L. De Pascale and P. Gori-Giorgi, Optimal-transport formulation of electronic density-functional theory. Phys. Rev. A 85 (2012) 062502. [Google Scholar]
  4. G. Carlier, On a class of multidimensional optimal transportation problems. J. Convex Anal. 10 (2003) 517–530. [MathSciNet] [Google Scholar]
  5. G. Carlier and B. Nazaret, Optimal transportation for the determinant. ESAIM: COCV 14 (2008) 678–698. [CrossRef] [EDP Sciences] [Google Scholar]
  6. M. Colombo, L. De Pascale and S. Di Marino, Multimarginal optimal transport maps for 1-dimensional repulsive costs. Canad. J. Math. (2013). [Google Scholar]
  7. M. Colombo and S. Di Marino, Equality between monge and kantorovich multimarginal problems with coulomb cost. Ann. Mat. Pura Appl. (2013) 1–14. [Google Scholar]
  8. C. Cotar, G. Friesecke and C. Klüppelberg, Density functional theory and optimal transportation with coulomb cost. Commun. Pure Appl. Math. 66 (2013) 548–599. [Google Scholar]
  9. G. Dal Maso, An introduction to Γ-convergence. Springer (1993). [Google Scholar]
  10. G. Friesecke, Ch.B. Mendl, B. Pass, C. Cotar and C. Klüppelberg, N-density representability and the optimal transport limit of the hohenberg−kohn functional. J. Chem. Phys. 139 (2013) 164–109. [Google Scholar]
  11. W. Gangbo and A. Swiech, Optimal maps for the multidimensional monge−kantorovich problem. Comm. Pure Appl. Math. 51 (1998) 23–45. [Google Scholar]
  12. N. Ghoussoub and A. Moameni, A self-dual polar factorization for vector fields. Comm. Pure Appl. Math. 66 (2013) 905–933. [Google Scholar]
  13. P. Gori-Giorgi and M. Seidl, Density functional theory for strongly-interacting electrons: perspectives for physics and chemistry. Phys. Chem. Chem. Phys. 12 (2010) 14405–14419. [CrossRef] [PubMed] [Google Scholar]
  14. P. Gori-Giorgi, M. Seidl and G. Vignale, Density-functional theory for strongly interacting electrons. Phys. Rev. Lett. 103 (2009) 166402. [CrossRef] [PubMed] [Google Scholar]
  15. H. Heinich, Problème de monge pour n probabilités. C. R. Math. 334 (2002) 793–795. [Google Scholar]
  16. P. Hohenberg and W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136 (1964) B864. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  17. H.G. Kellerer, Duality theorems for marginal problems. Probab. Theory Relat. Fields 67 (1984) 399–432. [Google Scholar]
  18. Walter Kohn and Lu Jeu Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140 (1965) A1133. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  19. E.H. Lieb. Density functionals for coulomb systems. Int J. Quantum Chem. 24 (1983) 243–277. [Google Scholar]
  20. Ch.B. Mendl and L. Lin, Kantorovich dual solution for strictly correlated electrons in atoms and molecules. Phys. Rev. B 87 (2013) 125106. [CrossRef] [Google Scholar]
  21. B. Pass, Uniqueness and monge solutions in the multimarginal optimal transportation problem. SIAM J. Math. Anal. 43 (2011) 2758–2775. [CrossRef] [MathSciNet] [Google Scholar]
  22. B. Pass, On the local structure of optimal measures in the multi-marginal optimal transportation problem. Calc. Var. Partial Differ. Equ. 43 (2012) 529–536. [Google Scholar]
  23. S.T. Rachev and L. Rüschendorf, Mass transportation problems. Probab. Appl. Springer-Verlag (1998), Vol. I. [Google Scholar]
  24. M. Seidl, Strong-interaction limit of density-functional theory. Phys. Rev. A 60 (1999) 4387. [Google Scholar]
  25. M. Seidl, P. Gori-Giorgi and A. Savin, Strictly correlated electrons in density-functional theory: A general formulation with applications to spherical densities. Phys. Rev. A 75 (2007) 042511. [Google Scholar]
  26. M. Seidl, J.P. Perdew and M. Levy, Strictly correlated electrons in density-functional theory. Phys. Rev. A 59 (1999) 51. [Google Scholar]

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