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dc.contributor.authorBonheure, Denis
dc.contributor.authorDolbeault, Jean
dc.contributor.authorEsteban, Maria J.
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.urihttps://basepub.dauphine.fr/handle/123456789/18555
dc.language.isoenen
dc.subjectHardy-Sobolev inequalitiesen
dc.subjectCaffarelli-Kohn-Nirenberg inequalitiesen
dc.subjectmagnetic ringsen
dc.subjectmagnetic Schrödinger operatoren
dc.subjectAharonov-Bohm magnetic potentialen
dc.subjectradial symmetryen
dc.subjectsymmetry breakingen
dc.subjectmagnetic Hardy-Sobolev inequalityen
dc.subjectmagnetic interpolation inequalityen
dc.subjectoptimal constantsen
dc.subject.ddc515en
dc.titleSymmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fieldsen
dc.typeDocument de travail / Working paper
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.en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages17en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02003872en
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2019-02
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2019-03-25T10:31:41Z
hal.person.labIds255058
hal.person.labIds60
hal.person.labIds60
hal.person.labIds4553
hal.person.labIds7772


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