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.
Citation
Gisèle R. Goldstein. Jerome A. Goldstein. Naima Naheed. "A Convex Minorant Problem Arising in Electron Density Theory." Commun. Math. Anal. 8 (2) 92 - 102, 2010.
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