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A variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalities

dc.contributor.authorAntunes, Pedro R. S.
dc.contributor.authorBenguria, Rafael
dc.contributor.authorLotoreichik, Vladimir
dc.contributor.authorOurmières-Bonafos, Thomas
dc.date.accessioned2021-05-07T10:30:34Z
dc.date.available2021-05-07T10:30:34Z
dc.date.issued2021
dc.description.abstractWe investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szeg\"o type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. The paper is complemented with strong numerical evidences supporting the existence of a Faber-Krahn type inequality.pt_PT
dc.description.versioninfo:eu-repo/semantics/acceptedVersionpt_PT
dc.identifier.issn0010-3616 (Print)
dc.identifier.issn1432-0916 (Online)
dc.identifier.urihttp://hdl.handle.net/10400.2/10710
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringerpt_PT
dc.titleA variational formulation for Dirac operators in bounded domains: applications to spectral geometric inequalitiespt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.titleCommunications in Mathematical Physicspt_PT
person.familyNameAntunes
person.familyNameBenguria
person.familyNameLotoreichik
person.givenNamePedro
person.givenNameRafael
person.givenNameVladimir
person.identifier.ciencia-id6710-138C-A69D
person.identifier.orcid0000-0003-1969-1860
person.identifier.orcid0000-0002-0696-0876
person.identifier.orcid0000-0003-1739-3819
person.identifier.ridM-2406-2015
person.identifier.scopus-author-id55346859100
person.identifier.scopus-author-id6701690271
person.identifier.scopus-author-id26536200200
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
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relation.isAuthorOfPublicationa1348657-91d6-48b4-973c-d0146857850d
relation.isAuthorOfPublication23498864-4ca6-48e4-b5ca-7db90de888f5
relation.isAuthorOfPublication.latestForDiscoverybef314d2-4a78-4fba-aecd-9f4e8e19e70c

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