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Regularity for the optimal compliance problem with length penalization

dc.contributor.authorChambolle, Antonin
HAL ID: 184536
ORCID: 0000-0002-9465-4659
dc.contributor.authorLamboley, Jimmy
HAL ID: 6598
dc.contributor.authorLemenant, Antoine
HAL ID: 743071
dc.contributor.authorStepanov, Eugene
dc.date.accessioned2017-12-01T12:49:17Z
dc.date.available2017-12-01T12:49:17Z
dc.date.issued2017
dc.identifier.issn0036-1410
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17144
dc.language.isoenen
dc.subjectcompliance
dc.subjectshape optimisation
dc.subjectregularity
dc.subjectMumford-Shah
dc.subject.ddc515en
dc.titleRegularity for the optimal compliance problem with length penalization
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe prove some regularity results for a connected set S in the planar domain O, which minimizes the compliance of its complement O\S, plus its length. This problem, interpreted as to find the best location for attaching a membrane subject to a given external force f so as to minimize the compliance, can be seen as an elliptic PDE version of the average distance problem/irrigation problem (in a penalized version rather than a constrained one), which has been extensively studied in the literature. We prove that minimizers consist of a finite number of smooth curves meeting only by three at 120 degree angles, containing no loop, and possibly touching the boundary of the domain only tangentially. Several new technical tools together with the classical ones are developed for this purpose.
dc.relation.isversionofjnlnameSIAM Journal on Mathematical Analysis
dc.relation.isversionofjnlvol49
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages1166–1224
dc.relation.isversionofdoi10.1137/16M1070578
dc.relation.isversionofjnlpublisherSociety for Industrial and Applied Mathematics
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.updated2017-12-15T15:10:31Z


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