@article{dc4e97c3a0ce4405af332c0c1a62a4f0,
title = "Dimensionality of Local Minimizers of the Interaction Energy",
abstract = "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. {\textcopyright} 2013 Springer-Verlag Berlin Heidelberg.",
author = "D. Balagu{\'e} and Carrillo, {J. A.} and T. Laurent and G. Raoul",
note = "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.",
year = "2013",
month = may,
day = "22",
doi = "10.1007/s00205-013-0644-6",
language = "English (US)",
volume = "209",
pages = "1055--1088",
journal = "Archive for Rational Mechanics and Analysis",
issn = "0003-9527",
publisher = "Springer New York",
number = "3",
}