hal.structure.identifier CEntre de REcherches en MAthématiques de la DEcision [CEREMADE] dc.contributor.author Borrelli, William dc.date.accessioned 2020-05-06T13:59:23Z dc.date.available 2020-05-06T13:59:23Z dc.date.issued 2018 dc.identifier.issn 0022-2488 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/20706 dc.language.iso en en dc.subject electron transport en dc.subject Graphene en dc.subject Nonlinear Dirac equation en dc.subject Self-consistent model en dc.subject.ddc 515 en dc.title Multiple solutions for a self-consistent Dirac equation in two dimensions en dc.type Article accepté pour publication ou publié dc.description.abstracten This 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.isversionofjnlname Journal of Mathematical Physics dc.relation.isversionofjnlvol 59 en dc.relation.isversionofjnlissue 4 en dc.relation.isversionofjnldate 2018-04 dc.relation.isversionofdoi 10.1063/1.5005998 en dc.relation.isversionofjnlpublisher American Institute of Physics en dc.subject.ddclabel Analyse en dc.relation.forthcoming non en dc.relation.forthcomingprint non en dc.description.ssrncandidate non en dc.description.halcandidate non en dc.description.readership recherche en dc.description.audience International en dc.relation.Isversionofjnlpeerreviewed oui en dc.relation.Isversionofjnlpeerreviewed oui en dc.date.updated 2020-05-06T13:57:14Z hal.author.function aut
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