Nonlocal anisotropic Riesz interactions with a physical confinement
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911049353003008 |
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| author | Mora, Maria Giovanna Rondi, Luca Scardia, Lucia Tolotti, Edoardo Giovanni |
| author_facet | Mora, Maria Giovanna Rondi, Luca Scardia, Lucia Tolotti, Edoardo Giovanni |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal anisotropic Riesz interactions with a physical confinement Mora, Maria Giovanna Rondi, Luca Scardia, Lucia Tolotti, Edoardo Giovanni Analysis of PDEs 31A15 (Primary) 49K20 (Secondary) 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. |
| title | Nonlocal anisotropic Riesz interactions with a physical confinement |
| topic | Analysis of PDEs 31A15 (Primary) 49K20 (Secondary) |
| url | https://arxiv.org/abs/2507.07710 |