Nonlocal anisotropic Riesz interactions with a physical confinement
Analysis of PDEs
2025-07-11 v1
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.
Keywords
Cite
@article{arxiv.2507.07710,
title = {Nonlocal anisotropic Riesz interactions with a physical confinement},
author = {Maria Giovanna Mora and Luca Rondi and Lucia Scardia and Edoardo Giovanni Tolotti},
journal= {arXiv preprint arXiv:2507.07710},
year = {2025}
}