Dimensionality of Local Minimizers of the Interaction Energy

Journal article (2013)

Authors

D. Balagué Guardia Universitat Autònoma de Barcelona
Jose Antonio Carrillo Imperial College London
Thomas Laurent University of California
Gael Raoul CNRS
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Hausdorff dimension Local Minimizer Interaction Energy Borel Probability Measure Attractive Potential
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Published Date

2013

Language

English

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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.