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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorBorrelli, William
dc.date.accessioned2020-05-06T13:59:23Z
dc.date.available2020-05-06T13:59:23Z
dc.date.issued2018
dc.identifier.issn0022-2488
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20706
dc.language.isoenen
dc.subjectelectron transporten
dc.subjectGrapheneen
dc.subjectNonlinear Dirac equationen
dc.subjectSelf-consistent modelen
dc.subject.ddc515en
dc.titleMultiple solutions for a self-consistent Dirac equation in two dimensionsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is devoted to the variational study of an effective model for the electron transport in a graphene sample. We prove the existence of infinitely many stationary solutions for a nonlin-ear Dirac equation which appears in the WKB limit for the Schrödinger equation describing the semi-classical electron dynamics. The interaction term is given by a mean field, self-consistent potential which is the trace of the 3D Coulomb potential. Despite the nonlinearity being 4-homogeneous, compactness issues related to the limiting Sobolev embedding H12(Ω,C)→L4(Ω,C) are avoided thanks to the regular-ization property of the operator $(-\Delta)^{-\frac{1}{2}$. This also allows us to prove smoothness of the solutions. Our proof follows by direct arguments.en
dc.relation.isversionofjnlnameJournal of Mathematical Physics
dc.relation.isversionofjnlvol59en
dc.relation.isversionofjnlissue4en
dc.relation.isversionofjnldate2018-04
dc.relation.isversionofdoi10.1063/1.5005998en
dc.relation.isversionofjnlpublisherAmerican Institute of Physicsen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2020-05-06T13:57:14Z
hal.author.functionaut


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