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Keller estimates of the eigenvalues in the gap of Dirac operators

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorGontier, David
HAL ID: 11393
ORCID: 0000-0001-8648-7910
hal.structure.identifierDepartamento de Matemática Aplicada y Ciencias de la Computación
dc.contributor.authorPizzichillo, Fabio
hal.structure.identifierDepartamento de Ingeniería Matemática [Santiago] [DIM]
hal.structure.identifierCenter for Mathematical Modeling [CMM]
dc.contributor.authorVan Den Bosch, Hanne
dc.date.accessioned2022-11-07T14:02:52Z
dc.date.available2022-11-07T14:02:52Z
dc.date.issued2022
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/23101
dc.language.isoenen
dc.subjectDirac operatorsen
dc.subjectpotentialen
dc.subjectspectral gapen
dc.subjecteigenvaluesen
dc.subjectground stateen
dc.subjectmin-max principleen
dc.subjectBirman-Schwinger operatoren
dc.subjectdomainen
dc.subjectself-adjoint operatorsen
dc.subjectKeller estimateen
dc.subjectinterpolationen
dc.subjectGagliardo-Nirenberg-Sobolev inequalityen
dc.subjectKerr nonlinearityen
dc.subject.ddc515en
dc.titleKeller estimates of the eigenvalues in the gap of Dirac operatorsen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe estimate the lowest eigenvalue in the gap of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart for Dirac operators of the Keller estimates for the Schrödinger operator, which are equivalent to Gagliardo-Nirenberg-Sobolev interpolation inequalities. Domain, self-adjointness, optimality and critical values of the norms are addressed, while the optimal potential is given by a Dirac equation with a Kerr nonlinearity. A new critical bound appears, which is the smallest value of the norm of the potential for which eigenvalues may reach the bottom of the gap in the essential spectrum. Most of our result are established in the Birman-Schwinger reformulation of the problem.en
dc.identifier.citationpages35en
dc.relation.ispartofseriestitleCahiers du CEREMADEen
dc.subject.ddclabelAnalyseen
dc.identifier.citationdate2022
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2022-11-07T13:51:22Z
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