Optimal transport with Coulomb cost and the semiclassical limit of density functional theory, J. Éc. Polytech. Math, vol.4, pp.909-934, 2017. ,
Dissociating limit in Density Functional Theory with Coulomb optimal transport cost ,
Continuity and estimates for multimarginal optimal transportation problems with singular costs, Appl. Math. Optim, vol.78, issue.1, pp.185-200, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01358148
Optimal-transport formulation of electronic density-functional theory, Phys. Rev. A, vol.85, pp.62502-62503, 2012. ,
Numerical methods for a Kohn-Sham density functional model based on optimal transport, J. Chem. Theory Comput, vol.10, pp.4360-4368, 2014. ,
Continuity of multi-marginal optimal transport with repulsive cost, 2019. ,
Klüppelberg: Density functional theory and optimal transportation with Coulomb cost, Comm. Pure Appl. Math, vol.66, issue.4, pp.548-599, 2013. ,
Klüppelberg: Smoothing of transport plans with fixed marginals and rigorous semiclassical limit of the Hohenberg-Kohn functional, Arch. Ration. Mech. Anal, vol.228, issue.3, pp.891-922, 2018. ,
Next-order asymptotic expansion for N -marginal optimal transport with Coulomb and Riesz costs, Adv. Math ,
Optimal transport with Coulomb cost. Approximation and duality, ESAIM Math. Model. Numer. Anal, vol.49, issue.6, pp.1643-1657, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01941414
Nenna: Paper in preparation and Personal Communication, 2019. ,
A short proof of the ionization conjecture in Müller theory, Contemp. Math. of Amer. Math. Soc, vol.717, pp.1-12, 2018. ,
, The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory, vol.71, pp.577-614, 2018.
Duality theorems for marginal problems, Probability Theory and Related Fields, vol.67, pp.399-432, 1984. ,
Large deviation principle for empirical fields of Log and Riesz gases. Invent. math, vol.210, pp.645-757, 2017. ,
Semi-classical limit of the Levy-Lieb functional in Density Functional Theory, C. R. Math. Acad. Sci. Paris, vol.356, issue.4, pp.449-455, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01534079
Seiringer: Statistical mechanics of the Uniform Electron Gas, J. Éc. Polytech. Math, vol.5, pp.79-116, 2018. ,
Density functionals for Coulomb systems, Internat. J. Quantum Chem, vol.24, issue.3, pp.243-277, 1983. ,
Systems of points with Coulomb interactions, Eur. Math. Soc. Newsl. No, vol.110, pp.16-21, 2018. ,
Next order asymptotics and renormalized energy for Riesz interactions, J. Inst. Math. Jussieu, vol.16, issue.3, pp.501-569, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01377806
, The ionization conjecture in Hartree-Fock theory, vol.158, pp.509-576, 2003.
Proof of the ionization conjecture in a reduced Hartree-Fock model, Invent. Math, vol.104, issue.2, pp.291-311, 1991. ,
Topics in optimal transportation, Graduate Studies in Mathematics, vol.58, 2003. ,
, 83957 La Garde Cedex -FRANCE bouchitte@univ-tln, 20132.
Pontecorvo 5, 56127 Pisa -ITALY giuseppe, Laboratoire IMATH, Université de Toulon BP 20132, 83957 La Garde Cedex -FRANCE champion@univ-tln ,
Università di Firenze Viale Morgagni 67/a, 50134 Firenze -ITALY luigi, Dipartimento di Matematica e Informatica ,