Free Access
Volume 25, 2019
Article Number 62
Number of page(s) 21
Published online 25 October 2019
  1. U. Bindini and L. De Pascale, Optimal transport with Coulomb cost and the semiclassical limit of density functional theory. J. Éc. Polytech. Math. 4 (2017) 909–934. [CrossRef] [Google Scholar]
  2. A. Braides, Gamma-Convergence for Beginners, Vol. 22. Clarendon Press, Oxford (2002). [CrossRef] [Google Scholar]
  3. G. Buttazzo, T. Champion and L. De Pascale, Continuity and estimates for multimarginal optimal transportation problems with singular costs. Appl. Math. Optim. 78 (2018) 185–200. [Google Scholar]
  4. 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]
  5. H. Chen, G. Friesecke and C. B. Mendl, Numerical methods for a kohn–sham density functional model based on optimal transport. J. Chem. Theory Comput. 10 (2014) 4360–4368. [Google Scholar]
  6. M. Colombo and F. Stra, Counterexamples to multimarginal optimal transport maps with coulomb cost and radial measures. Math. Models Methods Appl. Sci. 26 (2016) 1025–1049. [Google Scholar]
  7. L. Cort, D. Karlsson, G. Lani and R. van Leeuwen, Time-dependent density-functional theory for strongly interacting electrons. Phys. Rev. A 95 (2017) 042505. [Google Scholar]
  8. C. Cotar, G. Friesecke and C. Klüppelberg, Density functional theory and optimal transportation with coulomb cost. Comm. Pure Appl. Math. 66 (2013) 548–599. [CrossRef] [Google Scholar]
  9. C. Cotar, G. Friesecke and C. Klüppelberg, Smoothing of transport plans with fixed marginals and rigorous semiclassical limit of the Hohenberg-Kohn functional. Arch. Ration. Mech. Anal. 228 (2018) 891–922. [Google Scholar]
  10. L. De Pascale, Optimal transport with coulomb cost. approximation and duality. ESAIM: M2AN 49 (2015) 1643–1657. [CrossRef] [EDP Sciences] [Google Scholar]
  11. S. Di Marino, L. De Pascale and M. Colombo, Multimarginal optimal transport maps for 1-dimensional repulsive costs. Can. J. Math. 67 (2015) 350–368. [CrossRef] [Google Scholar]
  12. S. Di Marino, A. Gerolin and L. Nenna, Topological Optimization and Optimal Transport In the Applied Sciences. De Gruyter (2017). [Google Scholar]
  13. G. Friesecke, C. 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) 164109. [Google Scholar]
  14. W. Gangbo and V. Oliker, Existence of optimal maps in the reflector-type problems. ESAIM: COCV 13 (2007) 93–106. [CrossRef] [EDP Sciences] [Google Scholar]
  15. A. Gerolin, A. Kausamo and T. Rajala, Non-existence of optimal transport maps for the multi-marginal repulsive harmonic cost. Preprint arXiv:1805.00417 (2018). [Google Scholar]
  16. 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]
  17. W. E. Hartnett and A. H. Kruse, Differentiation of set functions using Vitali coverings. Trans. Amer. Math. Soc. 96 (1960) 185–209. [CrossRef] [Google Scholar]
  18. P. Hohenberg and W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136 (1964) B864. [Google Scholar]
  19. A. Käenmäki, T. Rajala and V. Suomala, Existence of doubling measures via generalised nested cubes. Proc. Am. Math. Soc. 140 (2012) 3275–3281. [Google Scholar]
  20. H. G. Kellerer, Duality theorems for marginal problems. Z. Wahrscheinlichkeitstheor. Verw. Geb. 67 (1984) 399–432. [CrossRef] [MathSciNet] [Google Scholar]
  21. G. Lani, S. Di Marino, A. Gerolin, R. van Leeuwen, and P. Gori-Giorgi, The adiabatic strictly-correlated-electrons functional: kernel and exact properties. Phys. Chem. Chem. Phys. 18 (2016) 21092–21101. [CrossRef] [PubMed] [Google Scholar]
  22. M. Levy, 2016 Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem. Proc. Nati. Acad. Sci. 12 (76) 6062–6065. [Google Scholar]
  23. M. Lewin, Semi-classical limit of the Levy-Lieb functional in density functional theory. C. R. Math. Acad. Sci. Paris 356 (2018) 449–455. [CrossRef] [Google Scholar]
  24. E. H. Lieb, Density functionals for coulomb systems, in Inequalities. Springer, Berlin, Heidelberg (2002) 269–303. [CrossRef] [Google Scholar]
  25. F. Malet and P. Gori-Giorgi, Strong in Kohn-Sham density functional theory. Phys. Rev. Lett. 109 (2012) 246402. [CrossRef] [PubMed] [Google Scholar]
  26. M. Seidl, Strong-interaction limit of density-functional theory. Phys. Rev. A, 60 (1999) 4387. [Google Scholar]
  27. M. Seidl, S. Di Marino, A. Gerolin, L. Nenna, K. Giesbertz and P. Gori-Giorgi, The strictly-correlated electron functional for spherically symmetric systems revisited. Preprint arXiv:1702.05022 (2017). [Google Scholar]
  28. 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]
  29. C. Villani. Optimal Transport: old and New, Vol. 338. Springer Science & Business Media, Berlin, Heidelberg (2008). [Google Scholar]
  30. X.-J. Wang, On the design of a reflector antenna ii. Calc. Var. Partial Differ. Equ. 20 (2004) 329.–341. [Google Scholar]

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