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. © 2013 Springer-Verlag Berlin Heidelberg.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1055-1088 |
| Number of pages | 34 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 209 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 22 2013 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged 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.