Ground-states for the liquid drop and TFDW models with long-range attraction.

We prove that both the liquid drop model in ℝ³ with an attractive background nucleus and the Thomas-Fermi-Dirac-von Weizsäcker (TFDW) model attain their groundstates for all masses as long as the external potential V(x) in these models is of long range, that is, it decays slower than Newtonian (e.g., V(χ)>>|χ|-1 for large |χ|.) For the TFDW model, we adapt classical concentration-compactness arguments by Lions, whereas for the liquid drop model with background attraction, we utilize a recent compactness result for sets of finite perimeter by Frank and Lieb. [ABSTRACT FROM AUTHOR]