A convexified energy functional forthe Fermi-Amaldi correction

Gisèle Ruiz Goldstein; Jerome A. Goldstein; Naima Naheed

doi:10.3934/dcds.2010.28.41

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2010, Volume 28, Issue 1: 41-65. Doi: 10.3934/dcds.2010.28.41

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A convexified energy functional for the Fermi-Amaldi correction

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

Received: October 2009

Revised: January 2010

Published: March 2010

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Abstract

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 $N_{1}.$

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Mathematics Subject Classification: Primary: 35J47, 35J91, 49S05; Secondary: 81Q99, 81V55, 92E10.

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