Explicit minimisers for anisotropic Riesz energies
In this paper we characterise the energy minimisers of a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisotropic. In particular we show that, if the Fourier transform of the repulsive potential is positive, the minimiser is supported on a fully-dimensional ellipsoid, and its density is given by a Barenblatt-type profile. Our technique of proof is based on a Fourier representation of the potential of such measures, that extends a previous formula established by some of the authors in the Coulomb case.
Authors
- Lucia Scardia (ORCID: https://orcid.org/0000-0003-2957-043X)
- Rupert L. Frank (ORCID: https://orcid.org/0000-0001-7973-4688)
- Luca Rondi (ORCID: https://orcid.org/0000-0002-8107-2983)
- Maria Giovanna Mora (ORCID: https://orcid.org/0000-0002-7456-0065)
- José Lamarca Mateu (ORCID: https://orcid.org/0000-0001-8402-375X)
- Joan Verdera
Institutions
- California Institute of Technology (US)
- Universitat Autònoma de Barcelona (ES)
- University of Pavia (IT)
- Heriot-Watt University (GB)
- Centre de Recerca Matemàtica (ES)
- Munich Center for Quantum Science and Technology (DE)
- Ludwig-Maximilians-Universität München (DE)
Publication Details
- Journal
- Calculus of Variations and Partial Differential Equations
- Published
- 2025-12-13
- DOI
- https://doi.org/10.1007/s00526-025-03185-1
- Primary Topic
- Nonlinear Partial Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00