Communications in Mathematical Analysis

A Convex Minorant Problem Arising in Electron Density Theory

Gisèle R. Goldstein, Jerome A. Goldstein, and Naima Naheed

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Abstract

We find the largest convex minorant of the function

\begin{equation*} F\left( x,y\right) =ax^{2}+xy+by^{2} \end{equation*}

where $a,b$ are positive constants and $x\geq 0,\ y\geq 0$. We explain how the problem is closely connected with finding the ground state Thomas-Fermi electron density for a spin polarized quantum mechanical system with the Fermi-Amaldi correction.

Article information

Source
Commun. Math. Anal., Volume 8, Number 2 (2010), 92-102.

Dates
First available in Project Euclid: 21 April 2010

Permanent link to this document
https://projecteuclid.org/euclid.cma/1271890670

Mathematical Reviews number (MathSciNet)
MR2569956

Zentralblatt MATH identifier
1189.26020

Subjects
Primary: 52A41: Convex functions and convex programs [See also 26B25, 90C25] 26B25: Convexity, generalizations
Secondary: 81Q99: None of the above, but in this section 81V55: Molecular physics [See also 92E10] 92E10: Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

Keywords
Convex minorant Thomas-Fermi theory Fermi-Amaldi correction ground state electron density

Citation

Goldstein, Gisèle R.; Goldstein, Jerome A.; Naheed, Naima. A Convex Minorant Problem Arising in Electron Density Theory. Commun. Math. Anal. 8 (2010), no. 2, 92--102. https://projecteuclid.org/euclid.cma/1271890670


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