A convexified energy functional for the Fermi-Amaldi correction
Consider the Thomas-Fermi energy functional E for a spin polarized atom or molecule with N1 [resp. N2] spin up [resp. spin down] electrons and total positive molecular charge Z. Incorporating the Fermi-Amaldi correction as Benilan, Goldstein and Goldstein did, E is not convex. By replacing E by a well-motivated convex minorant ε, we prove that £ has a unique minimizing density (ρ1, ρ2) when N1 + N2 ≤ Z + 1 and N2 is close to N 1.
Discrete and Continuous Dynamical Systems
Goldstein, G., Goldstein, J., & Naheed, N. (2010). A convexified energy functional for the Fermi-Amaldi correction. Discrete and Continuous Dynamical Systems, 28 (1), 41-65. https://doi.org/10.3934/dcds.2010.28.41