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arXiv · 2507.07710

Nonlocal anisotropic Riesz interactions with a physical confinement

Maria Giovanna Mora·Luca Rondi·Lucia Scardia·Edoardo Giovanni Tolotti
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Abstract

In this work we fully characterize, in any space dimension, the minimizer of a class of nonlocal and anisotropic Riesz energies defined over probability measures supported on ellipsoids. In the super-Coulombic and Coulombic regime, we prove that the minimizer is independent of the anisotropy. In contrast, in the sub-Coulombic regime we show that this property fails: we exhibit an example of anisotropy for which the isotropic minimizer is not optimal. In order to prove our main result, we provide a formula for the potential inside an ellipsoid, valid in any space dimension and involving the hypergeometric function.

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Maria Giovanna Mora, Luca Rondi, Lucia Scardia, Edoardo Giovanni Tolotti. 2025-07-10. Nonlocal anisotropic Riesz interactions with a physical confinement. https://arxiv.org/abs/2507.07710

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