Calculus of Variations and Geometric Measure Theory

R. Simione - D. SlepĨev - I. Topaloglu

Existence of Ground States of Nonlocal-Interaction Energies

created by topaloglu1 on 03 Aug 2019



Inserted: 3 aug 2019

Year: 2014

ArXiv: 1405.5146 PDF


We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that this condition is closely related to the notion of stability (i.e. $H$-stability) of pairwise interaction potentials. Our approach uses the direct method of the calculus of variations.