Published Paper

Inserted: 11 jul 2025
Last Updated: 18 aug 2026

Journal: SIAM Journal on Mathematical Analysis
Volume: 58
Number: 4
Year: 2026
Doi: https://doi.org/10.1137/25M1783606

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.