Year: 2025
Type: article
Abstract: 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.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funders: National Science Foundation, Istituto Nazionale di Alta Matematica "Francesco Severi", Heriot-Watt University, European Commission, Deutsche Forschungsgemeinschaft, Generalitat de Catalunya, Università degli Studi di Pavia, Ministerio de Ciencia e Innovación, Ministero dell'Università e della Ricerca, Engineering and Physical Sciences Research Council
Awards: Variational Methods in Mathematical Physics and Analysis, G1768993395, G1889978188, G2098996113, G2430181592, G2474135926, Generalised and Low-Regularity Solutions of Nonlinear Partial Differential Equations, G4617604447, G4710139657, Mathematical theory of polycrystalline materials, G5141357660, G5245466801, G5341450975, TRR 352: Mathematik der VielteilchenQuantensysteme und ihrer kollektiven Phänomene, G7924212968, G8577275559, G8620905599, EXC 2111: Munich Center for Quantum Science and Technology (MCQST), G8908719260, G972786147
OpenAlex ID: W4417427256