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dc.contributor.authorLamboley, Jimmy
HAL ID: 6598
dc.contributor.authorFragalà, Ilaria
dc.contributor.authorBucur, Dorin
dc.date.accessioned2011-02-14T13:16:16Z
dc.date.available2011-02-14T13:16:16Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/5705
dc.language.isoenen
dc.subjectcapacityen
dc.subjectshape derivativesen
dc.subjectoptimizationen
dc.subjectconcavity inequalitiesen
dc.subjectconvex bodiesen
dc.subject.ddc516en
dc.titleOptimal convex shapes for concave functionalsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDipartimento di Matematica Francesco Brioschi Politecnico di Milano;Italie
dc.contributor.editoruniversityotherLaboratoire de Mathématiques (LAMA) CNRS : UMR5127 – Université de Savoie;France
dc.description.abstractenMotivated by a long-standing conjecture of Polya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application to isoperimetriclike inequalities. As a byproduct of this approach we also obtain a quantitative version of the Kneser-Süss inequality. Finally, for a large class of functionals involving Dirichlet energies and the surface measure, we perform a local analysis of strictly convex portions of the boundary via second order shape derivatives. This allows in particular to exclude the presence of smooth regions with positive Gauss curvature in an optimal shape for Polya-Szegö problem.en
dc.relation.isversionofjnlnameESAIM. COCV
dc.relation.isversionofjnlvol18
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages693-711
dc.relation.isversionofdoihttp://dx.doi.org/10.1051/cocv/2011167
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00564691/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherEDP Sciences
dc.subject.ddclabelGéométrieen


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