Geodesic
Existence of a minimizer for the quasi-relativistic Kohn-Sham model
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the standard and extended Kohn-Sham models for quasi-relativistic N-electron Coulomb systems; that is, systems where the kinetic energy of the electrons is given by the quasi-relativistic operator $$ \sqrt{-\alpha^{-2}\Delta_{x_n}+\alpha^{-4}}-\alpha^{-2}. $$ For spin-unpolarized systems in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge $Z_{\hbox{tot}}$ of K nuclei is greater than N-1 and that $Z_{\hbox{tot}}$ is smaller than a critical charge $Z_{\hbox{c}}=2 \alpha^{-1} \pi^{-1}$.
Classification : 35J60, 47J10, 58Z05, 81V55
Keywords: Kohn-Sham equations, ground state, variational methods, concentration-compactness, density operators 
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     author = {Argaez, Carlos and Melgaard, Michael},
     title = {Existence of a minimizer for the quasi-relativistic {Kohn-Sham} model},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a15/}
}
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Argaez, Carlos; Melgaard, Michael. Existence of a minimizer for the quasi-relativistic Kohn-Sham model. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a15/