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A Convex Minorant Problem Arising in Electron Density Theory

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

A Convex Minorant Problem Arising in Electron Density Theory

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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.