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dc.contributor.authorButtazzo, Giuseppe
dc.contributor.authorCarlier, Guillaume
dc.contributor.authorComte, Myriam
dc.date.accessioned2010-02-15T10:34:52Z
dc.date.available2010-02-15T10:34:52Z
dc.date.issued2007-03
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3452
dc.language.isoenen
dc.subjectCheeger setsen
dc.subjectp-Laplacian approximationen
dc.subjectconcave penalizationen
dc.subject1-Laplacian type operatorsen
dc.subject.ddc515en
dc.titleOn the selection of maximal Cheeger setsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenGiven a bounded open subset Ω of ℝd and two positive weight functions ƒ et g, the Cheeger sets of Ω are the subdomains C of finite perimeter of Ω that maximize the ratio ∫cƒ(x)dx/∫∂*c g(x)dΗd-1. Existence of Cheeger sets is a well-known fact. Uniqueness is a more delicate issue and is not true in general (although it holds when Ω is convex and ƒ ≡ g ≡ 1 as recently proved in [4]). However, there always exists a unique maximal (in the sense of inclusion) Cheeger set and this paper addresses the issue of how to determine this maximal set. We show that in general the approximation by the p-Laplacian does not provide, as p → 1, a selection criterion for determining the maximal Cheeger set. On the contrary, a different perturbation scheme, based on the constrained maximization of ∫Ω ƒ(u-εΦ(u))dx for a strictly convex function Φ, gives, as ε→0, the desired maximal set.en
dc.relation.isversionofjnlnameDifferential and Integral Equations
dc.relation.isversionofjnlvol20en
dc.relation.isversionofjnlissue9en
dc.relation.isversionofjnldate2007-09
dc.relation.isversionofjnlpages991-1004en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00140075/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherKhayyam Publishingen
dc.subject.ddclabelAnalyseen


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