Existence of minimizers for Kohn-Sham within the Local Spin Density   Approximation
  The purpose of this article is to extend the work by Anantharaman and Canc\`es [1], and prove the existence of minimizers for the spin-polarized Kohn-Sham model in the presence of a magnetic field within the local spin density approximation. We show that for any magnetic field that vanishes at infinity, the existence of minimizers is ensured for neutral or positively charged systems. The proof relies on classical concentration-compactness techniques. 
David Gontier
math-ph math.MP