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Creators/Authors contains: "Carazzato, Davide"

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  1. ; ; (, Pure and Applied Analysis)
    We consider a non-local interaction energy over bounded densities of fixed mass m. We prove that under certain regularity assumptions on the interaction kernel these energies admit minimizers given by characteristic functions of sets when m is sufficiently small (or even for every m, in particular cases). We show that these assumptions are satisfied by particular interaction kernels in power-law form, and give a certain characterization of minimizing sets. Finally, following a recent result of Davies, Lim and McCann, we give sufficient conditions on the interaction kernel so that the minimizer of the energy over probability measures is given by Dirac masses concentrated on the vertices of a regular (N+1)-gon of side length 1 in R^N. 
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    Free, publicly-accessible full text available November 17, 2025
  2. ; ; (, ESAIM: Control, Optimisation and Calculus of Variations)
    We characterize the maximizers of a functional that involves the minimization of the Wasserstein distance between sets of equal volume. We prove that balls are the only maximizers by combining a symmetrization-by-reflection technique with the uniqueness of optimal transport plans. Further, in one dimension, we provide a sharp quantitative refinement of this maximality result. 
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