Calculus of Variations and Geometric Measure Theory

S. Alama - L. Bronsard - R. Choksi - I. Topaloglu

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

created by topaloglu1 on 03 Aug 2019



Inserted: 3 aug 2019

Year: 2017

ArXiv: 1707.06674 PDF


We prove that both the liquid drop model in $\mathbb{R}^3$ with an attractive background nucleus and the Thomas-Fermi-Dirac-von Weizs\"{a}cker (TFDW) model attain their ground-states \emph{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., $V(x)\gg
^{-1}$ for large $
$.) 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.