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Geometry of minimizers for the interaction energy with mildly repulsive potentials

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Title: Geometry of minimizers for the interaction energy with mildly repulsive potentials
Authors: Carrillo de la Plata, J
Figalli, A
Patacchini, FS
Item 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.
Issue Date: 18-Oct-2016
Date of Acceptance: 4-Oct-2016
URI: http://hdl.handle.net/10044/1/41900
DOI: https://dx.doi.org/10.1016/j.anihpc.2016.10.004
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/Funder: The Royal Society
Funder's Grant Number: WM120001
Keywords: 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
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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