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dc.contributor.authorCabré Vilagut, Xavier
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2021-04-20T09:35:29Z
dc.date.issued2020-02-04
dc.identifier.citationCabre, X. Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory. "Annali di matematica pura ed applicata", 4 Febrer 2020, vol. 199, p. 1979-1995.
dc.identifier.issn0373-3114
dc.identifier.urihttp://hdl.handle.net/2117/343976
dc.descriptionThe final publication is available at link.springer.com
dc.description.abstractFor nonnegative even kernels K, we consider the K-nonlocal perimeter functional acting on sets. Assuming the existence of a foliation of space made of solutions of the associated K-nonlocal mean curvature equation in an open set O¿Rn, we built a calibration for the nonlocal perimeter inside O¿Rn. The calibrating functional is a nonlocal null-Lagrangian. As a consequence, we conclude the minimality in O of each leaf of the foliation. As an application, we prove the minimality of K-nonlocal minimal graphs and that they are the unique minimizers subject to their own exterior data. As a second application of the calibration, we give a simple proof of an important result from the seminal paper of Caffarelli, Roquejoffre, and Savin, stating that minimizers of the fractional perimeter are viscosity solutions.
dc.format.extent17 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.otherNonlocal perimeter
dc.subject.otherCalibration
dc.subject.otherNull-Lagrangian
dc.subject.otherNonlocal minimal surfaces
dc.subject.otherViscosity solutions
dc.titleCalibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory
dc.typeArticle
dc.contributor.groupUniversitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions
dc.identifier.doi10.1007/s10231-020-00952-z
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::49 Calculus of variations and optimal control; optimization
dc.subject.amsClassificació AMS::53 Differential geometry
dc.relation.publisherversionhttps://link.springer.com/article/10.1007%2Fs10231-020-00952-z
dc.rights.accessRestricted access - confidentiality agreement
local.identifier.drac27267599
dc.description.versionPostprint (author's final draft)
dc.date.lift10000-01-01
local.citation.authorCabre, X.
local.citation.publicationNameAnnali di matematica pura ed applicata
local.citation.volume199
local.citation.startingPage1979
local.citation.endingPage1995


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