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.

Publication Title

Discrete and Continuous Dynamical Systems