Geometry of minimizers for the interaction energy with mildly repulsive potentials
File(s)geometry_global_minimisers4.pdf (347.63 KB)
Accepted version
Author(s)
Carrillo de la Plata, J
Figalli, A
Patacchini, FS
Type
Journal Article
Abstract
We show that the support of any local minimizer of the interaction energy consists
of isolated points whenever the interaction potential is of class C
2
and is mildly repulsive at
the origin; if moreover a minimizer is global, then its support is finite. For a particular class of
potentials we prove the existence of a uniform upper bound on the cardinal of the support of
a global minimizer. In the one-dimensional case we give quantitative bounds.
of isolated points whenever the interaction potential is of class C
2
and is mildly repulsive at
the origin; if moreover a minimizer is global, then its support is finite. For a particular class of
potentials we prove the existence of a uniform upper bound on the cardinal of the support of
a global minimizer. In the one-dimensional case we give quantitative bounds.
Date Issued
2016-10-18
Date Acceptance
2016-10-04
Citation
Annales de l Institut Henri Poincare-Analyse Non Lineaire, 2016, 34 (5), pp.1299-1308
ISSN
0294-1449
Publisher
Elsevier
Start Page
1299
End Page
1308
Journal / Book Title
Annales de l Institut Henri Poincare-Analyse Non Lineaire
Volume
34
Issue
5
Copyright Statement
© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
The Royal Society
Grant Number
WM120001
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Interaction energy
Local minimizers
Mild repulsion
LOCAL MINIMIZERS
NONLOCAL MODEL
AGGREGATION
0101 Pure Mathematics
0102 Applied Mathematics
General Mathematics
Publication Status
Published