arXiv Analytics

Sign in

arXiv:1405.5146 [math.AP]AbstractReferencesReviewsResources

Existence of Ground States of Nonlocal-Interaction Energies

Robert Simione, Dejan Slepčev, Ihsan Topaloglu

Published 2014-05-20, updated 2015-01-28Version 2

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.

Comments: This version is to appear in the J Stat Phys
Categories: math.AP
Subjects: 49J45, 82B21, 82B05, 35R09, 45K05
Related articles: Most relevant | Search more
arXiv:1902.01495 [math.AP] (Published 2019-02-04)
Existence and regularity of minimizers for nonlocal energy functionals
arXiv:0712.3386 [math.AP] (Published 2007-12-20, updated 2008-06-02)
On the symmetry of minimizers
arXiv:1511.01039 [math.AP] (Published 2015-11-03)
Regularity and the Behavior of Eigenvalues for Minimizers of a Constrained $Q$-tensor Energy for Liquid Crystals

Links

Toolbox