A convexified energy functional forthe Fermi-Amaldi correction

Gisèle Ruiz Goldstein; Jerome A. Goldstein; Naima Naheed

doi:10.3934/dcds.2010.28.41

Article Contents

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

This issue Previous Article Longtime behavior for a model of homogeneous incompressible two-phase flows Next Article The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials

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: September 30, 2009

Revised: December 31, 2009

Published: February 2010

Abstract Related Papers Cited by

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 $N_{1}.$

Keywords:

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

Citation:

Article Metrics

HTML views() PDF downloads(95) Cited by(0)

A convexified energy functional for the Fermi-Amaldi correction

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

A convexified energy functional for the Fermi-Amaldi correction

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content