dc.contributor.author
Mateu, J.
dc.contributor.author
Mora, M.G.
dc.contributor.author
Rondi, L.
dc.contributor.author
Scardia, L.
dc.contributor.author
Verdera, J.
dc.date.accessioned
2023-11-14T10:03:49Z
dc.date.accessioned
2024-09-19T14:35:02Z
dc.date.available
2023-11-14T10:03:49Z
dc.date.available
2024-09-19T14:35:02Z
dc.date.issued
2023-12-01
dc.identifier.uri
http://hdl.handle.net/2072/537046
dc.description.abstract
In this paper we consider a general class of anisotropic energies in three dimensions and give a complete characterisation of their minimisers. We show that, depending on the Fourier transform of the interaction potential, the minimiser is either the normalised characteristic function of an ellipsoid or a measure supported on a two-dimensional ellipse. In particular, it is always an ellipsoid if the transform is strictly positive, while when the Fourier transform is degenerate both cases can occur. Finally, we show an explicit example where loss of dimensionality of the minimiser does occur. © 2023 The Author(s)
eng
dc.description.sponsorship
Funding text 1: MGM is a member of GNAMPA–INdAM. JM and JV acknowledge support by Generalitat de Catalunya under the grant 2021-SGR-00071 and by Ministerio de Ciencia e Innovación under the grant PID2020-112881 GB-I00 and the Severo Ochoa and Maria de Maeztu grant CEX2020-001084-M . MGM acknowledges support by MIUR under the grant PRIN2017BTM7SN . LR acknowledges support by MIUR under the grant PRIN201758MTR2 and by GNAMPA-INdAM through 2022 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 MGM, LR, and LS to the Universitat Autònoma de Barcelona, whose kind hospitality is gratefully acknowledged.; Funding text 2: MGM is a member of GNAMPA–INdAM. JM and JV acknowledge support by Generalitat de Catalunya under the grant 2021-SGR-00071 and by Ministerio de Ciencia e Innovación under the grant PID2020-112881 GB-I00 and the Severo Ochoa and Maria de Maeztu grant CEX2020-001084-M. MGM acknowledges support by MIUR under the grant PRIN2017BTM7SN. LR acknowledges support by MIUR under the grant PRIN201758MTR2 and by GNAMPA-INdAM through 2022 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 MGM, LR, and LS to the Universitat Autònoma de Barcelona, whose kind hospitality is gratefully acknowledged.
dc.format.extent
28 p.
cat
dc.publisher
Elsevier (Academic Press Inc.)
cat
dc.relation.ispartof
Advances in Mathematics
cat
dc.rights
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Anisotropic interaction; Coulomb potential; Nonlocal energy; Potential theory
cat
dc.title
Explicit minimisers for anisotropic Coulomb energies in 3D
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/publishedVersion
cat
dc.identifier.doi
10.1016/j.aim.2023.109333
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
