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Estimates of First and Second Order Shape Derivatives in Nonsmooth Multidimensional Domains and Applications

dc.contributor.authorLamboley, Jimmy
HAL ID: 6598
dc.contributor.authorNovruzi, Arian
dc.contributor.authorPierre, Michel
HAL ID: 6510
dc.date.accessioned2017-12-01T13:07:25Z
dc.date.available2017-12-01T13:07:25Z
dc.date.issued2016
dc.identifier.issn0022-1236
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17146
dc.language.isoenen
dc.subjectshape optimization
dc.subjectoptimality conditions
dc.subjectconvexity constraint
dc.subjectShape derivative
dc.subjectSobolev estimates
dc.subjectregularity
dc.subjectenergy functional
dc.subject.ddc515en
dc.titleEstimates of First and Second Order Shape Derivatives in Nonsmooth Multidimensional Domains and Applications
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDE's around nonsmooth domains, essentially either Lipschitz or convex, or satisfying a uniform exterior ball condition. We prove rather sharp continuity results for these shape derivatives with respect to Sobolev norms of the boundary-traces of the displacements. With respect to previous results of this kind, the approach is quite different and is valid in any dimension $N\geq 2$. It is based on sharp regularity results for Poisson-type equations in such nonsmooth domains. We also enlarge the class of functionals and PDEs for which these estimates apply. Applications are given to qualitative properties of shape optimization problems under convexity constraints for the variable domains or their complement.
dc.relation.isversionofjnlnameJournal of Functional Analysis
dc.relation.isversionofjnlvol270
dc.relation.isversionofjnlissue7
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages2616-2652
dc.relation.isversionofdoi10.1016/j.jfa.2016.02.013
dc.relation.isversionofjnlpublisherAcademic Press
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-19T10:50:33Z


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