# American Institute of Mathematical Sciences

March  2010, 28(1): 41-65. doi: 10.3934/dcds.2010.28.41

## A convexified energy functional for the Fermi-Amaldi correction

 1 Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, United States, United States 2 Department of Mathematics and Computer Science, Benedict College, Columbia, SC 29204, United States

Received  October 2009 Revised  January 2010 Published  April 2010

Consider the Thomas-Fermi energy functional $E$ for a spin polarized atom or molecule with $N_{1}$ [resp. $N_{2}$] 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 $\mathcal{E}$ ,we prove that $\mathcal{E}$ has a unique minimizing density $( \rho _{1},\rho _{2}) \$ when $N_{1}+N_{2}\leq Z+1\$and $N_{2}\$is close to $N_{1}.$
Citation: Gisèle Ruiz Goldstein, Jerome A. Goldstein, Naima Naheed. A convexified energy functional for the Fermi-Amaldi correction. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 41-65. doi: 10.3934/dcds.2010.28.41
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