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Minimizers for an aggregation model with attractive-repulsive interaction
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We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that part of the remaining parameter regime all minimizers are uniform distributions on a surface of a sphere, thus showing concentration on a lower dimensional set. Our method of proof uses convexity estimates on hypergeometric functions.
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Cited by 2 Pith papers
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Existence of minimizers for interaction energies with external potentials
For essentially convex interaction kernels, a threshold condition on an auxiliary density guarantees existence, uniqueness, and compact support of minimizers in R^d and curved half-spaces; a counterexample shows the t...
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A family of explicit minimizers for interaction energies
For odd dimensions with interaction powers (a,b)=(3,2-d) and even dimensions with (3,1-d), the unique energy minimizer is given explicitly, with d=1,2,3 in elementary functions.
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