Opérateurs différentiels magnétiques : stabilité des trous dans le spectre,invariance du spectre essentiel et applications

We study here the problem of geometry optimization for a crystal in the Thomas–Fermi–Von Weizsäcker (TFW) solid-state setting, i.e., the problem of minimizing the TFW energy with respect to the periodic lattice defining the positions of the nuclei. We show the existence of such a minimum, and use for that purpose the TFW models of polymers and thin films defined in a previous work (X. Blanc and C. Le Bris, Adv. Differential Equations, 5, 977–1032, 2000).