dc.contributor.author
Frank, R.L.
dc.contributor.author
Mateu, Joan
dc.contributor.author
Mora, M.G.
dc.contributor.author
Rondi, L.
dc.contributor.author
Scardia, L.
dc.contributor.author
Verdera, J.
dc.date.accessioned
2026-01-21T11:49:12Z
dc.date.available
2026-01-21T11:49:12Z
dc.date.issued
2025-12-13
dc.identifier.uri
http://hdl.handle.net/2072/489161
dc.description.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.
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dc.description.sponsorship
RLF was partially supported through US National Science Foundation grant DMS1954995, as well as through the German Research Foundation through EXC-2111-390814868 and TRR 352-Project-ID 470903074. JM and JV have been partially supported by 2021SGR-00071 (Catalonia) and PID2024-155320NB-I00 (Mineco, Spain). MGM is a member of GNAMPA–INdAM. MGM acknowledges support from PRIN 2022 (Project no. 2022J4FYNJ), funded by MUR, Italy, and the European Union – Next Generation EU, Mission 4 Component 1 CUP F53D23002760006. LR is supported by the Italian MUR through the PRIN 2022 project n.2022B32J5C, under the National Recovery and Resilience Plan (PNRR), Italy, funded by the European Union - Next Generation EU, Mission 4 Component 1 CUP F53D23002710006, and by GNAMPA-INdAM through 2025 projects. LS acknowledges support by the EPSRC under the grants EP/V00204X/1 and EP/V008897/1. Part of this work was done during a visit of JM, MGM, LR, and JV to Heriot-Watt University, whose kind hospitality is gratefully acknowledged.
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dc.format.extent
25 p.
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dc.relation.ispartof
Calculus of Variations and Partial Differential Equations
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dc.rights
Attribution 4.0 International
*
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
*
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Riesz energies
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dc.title
Explicit minimisers for anisotropic Riesz energies
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1007/s00526-025-03185-1
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
