TY - JOUR
T1 - Dimensionality of Local Minimizers of the Interaction Energy
AU - Balagué, D.
AU - Carrillo, J. A.
AU - Laurent, T.
AU - Raoul, G.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1- 007-43
Acknowledgements: We would like to thanks James von Brecht for multiple insightful conversations concerning the numerical section of this paper. DB and JAC were supported by the projects Ministerio de Ciencia e Innovacion MTM2011-27739-C04-02 and 2009-SGR-345 from Agencia de Gestio d'Ajuts Universitaris i de Recerca-Generalitat de Catalunya. JAC acknowledges support from the Royal Society through a Wolfson Research Merit Award. This work was supported by Engineering and Physical Sciences Research Council grant number EP/K008404/1. GR was supported by Award No. KUK-I1- 007-43 of Peter A. Markowich, made by King Abdullah University of Science and Technology (KAUST). DB, JAC and GR acknowledge partial support from CBDif-Fr ANR-08-BLAN-0333-01 project. TL acknowledges the support from NSF Grant DMS-1109805.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2013/5/22
Y1 - 2013/5/22
N2 - In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated with a repulsive-attractive potential. We show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin. © 2013 Springer-Verlag Berlin Heidelberg.
AB - In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated with a repulsive-attractive potential. We show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin. © 2013 Springer-Verlag Berlin Heidelberg.
UR - http://hdl.handle.net/10754/597984
UR - http://link.springer.com/10.1007/s00205-013-0644-6
UR - http://www.scopus.com/inward/record.url?scp=84879262358&partnerID=8YFLogxK
U2 - 10.1007/s00205-013-0644-6
DO - 10.1007/s00205-013-0644-6
M3 - Article
VL - 209
SP - 1055
EP - 1088
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 3
ER -