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We consider minimization problems of the Thomas-Fermi-Dirac-von Weizsacker (TFDW) type, in which the Newtonian potential is perturbed by a background potential satisfying mild conditions and which ensures the existence of minimizers. We describe the structure of minimizing sequences for those variants, and obtain a more precise characterization of patterns in minimizing sequences for the TFDW functionals regularized by long-range perturbations.

Mass splitting in the Thomas–Fermi–Dirac–von Weizsäcker model with background potential