Dimensionality of Local Minimizers of the Interaction Energy
D. Balagué Guardia (Universitat Autònoma de Barcelona)
Jose Antonio Carrillo (Imperial College London)
Thomas Laurent (University of California)
Gael Raoul (Centre National de la Recherche Scientifique (CNRS))
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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.
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