KAUST Grant NumberKUK-I1- 007-43
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AbstractIn 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.
CitationBalagué D, Carrillo JA, Laurent T, Raoul G (2013) Dimensionality of Local Minimizers of the Interaction Energy. Archive for Rational Mechanics and Analysis 209: 1055–1088. Available: http://dx.doi.org/10.1007/s00205-013-0644-6.
SponsorsWe 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.