Show simple item record

dc.contributor.authorBonheure, Denis
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.contributor.authorEsteban, Maria J.
HAL ID: 738381
ORCID: 0000-0003-1700-9338
dc.contributor.authorLaptev, Ari
dc.contributor.authorLoss, Michael
dc.date.accessioned2019-03-25T10:48:46Z
dc.date.available2019-03-25T10:48:46Z
dc.date.issued2019
dc.identifier.issn0010-3616
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18555
dc.language.isoenen
dc.subjectHardy-Sobolev inequalities
dc.subjectCaffarelli-Kohn-Nirenberg inequalities
dc.subjectmagnetic rings
dc.subjectmagnetic Schrödinger operator
dc.subjectAharonov-Bohm magnetic potential
dc.subjectradial symmetry
dc.subjectsymmetry breaking
dc.subjectmagnetic Hardy-Sobolev inequality
dc.subjectmagnetic interpolation inequality
dc.subjectoptimal constants
dc.subject.ddc515en
dc.titleSymmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schrödinger operator involving an Aharonov-Bohm magnetic vector potential. We investigate the symmetry properties of the optimal potential for the corresponding magnetic Keller-Lieb-Thir-ring inequality. We prove that this potential is radially symmetric if the intensity of the magnetic field is below an explicit threshold, while symmetry is broken above a second threshold corresponding to a higher magnetic field. The method relies on the study of the magnetic kinetic energy of the wave function and amounts to study the symmetry properties of the optimal functions in a magnetic Hardy-Sobolev interpolation inequality. We give a quantified range of symmetry by a non-perturbative method. To establish the symmetry breaking range, we exploit the coupling of the phase and of the modulus and also obtain a quantitative result.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameCommunications in Mathematical Physics
dc.relation.isversionofjnldate2019
dc.relation.isversionofjnlpages17
dc.relation.isversionofdoi10.1007/s00220-019-03560-y
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02003872
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-12-09T13:11:11Z


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record