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dc.contributor.authorLamboley, Jimmy
dc.contributor.authorGazzola, Filippo
dc.contributor.authorFragalà, Ilaria
dc.date.accessioned2012-01-03T15:16:24Z
dc.date.available2012-01-03T15:16:24Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/7819
dc.language.isoenen
dc.subjectconvex shapesen
dc.subjectweb functionsen
dc.subjectshape optimizationen
dc.subjectisoperimetric inequalitiesen
dc.subject.ddc516en
dc.titleSharp bounds for the p-torsion of convex planar domainsen
dc.typeCommunication / Conférence
dc.contributor.editoruniversityotherDipartimento di Matematica Francesco Brioschi Politecnico di Milano Piazza Leonardo da Vinci, 32 20133 Milano;Italie
dc.description.abstractenWe obtain some sharp estimates for the $p$-torsion of convex planar domains in terms of their area, perimeter, and inradius. The approach we adopt relies on the use of web functions (i.e. functions depending only on the distance from the boundary), and on the behaviour of the inner parallel sets of convex polygons. As an application of our isoperimetric inequalities, we consider the shape optimization problem which consists in maximizing the $p$-torsion among polygons having a given number of vertices and a given area. A long-standing conjecture by Pólya-Szegö states that the solution is the regular polygon. We show that such conjecture is true within the subclass of polygons for which a suitable notion of ''asymmetry measure'' exceeds a critical threshold.en
dc.identifier.citationpages97-115en
dc.relation.ispartofseriestitleSpringer INdAM
dc.relation.ispartofseriesnumber2
dc.relation.ispartoftitleGeometric Properties for Parabolic and Elliptic PDE's
dc.relation.ispartofeditorAlvino, Angelo
dc.relation.ispartofeditorSakaguchi, Shigeru
dc.relation.ispartofeditorMagnanini, Rolando
dc.relation.ispartofpublnameSpringer
dc.relation.ispartofpublcityBerlin
dc.relation.ispartofdate2013
dc.relation.ispartofpages292
dc.relation.ispartofurlhttp://dx.doi.org/10.1007/978-88-470-2841-8
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00654228/fr/en
dc.description.sponsorshipprivatenonen
dc.subject.ddclabelGéométrieen
dc.relation.ispartofisbn978-88-470-2840-1
dc.relation.conftitleGeometric Properties for Parabolic and Elliptic PDE's
dc.relation.confcityCortone
dc.relation.confcountryItalie
dc.identifier.doihttp://dx.doi.org/10.1007/978-88-470-2841-8_7
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