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dc.contributor.authorSantambrogio, Filippo
dc.contributor.authorMorel, Jean-Michel
dc.date.accessioned2010-02-15T14:56:48Z
dc.date.available2010-02-15T14:56:48Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3463
dc.language.isoenen
dc.subjectbranched structureen
dc.subjectnetworken
dc.subject.ddc515en
dc.titleThe regularity of optimal irrigation patternsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenA branched structure is observable in draining and irrigation systems, in electric power supply systems and in natural objects like the blood vessels, the river basins or the trees. Recent approaches of these networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow s in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to sa with 0 < a < 1. The aim of this paper is to prove the regularity of paths (rivers, branches,...) when the irrigated measure is the Lebesgue density on a smooth open set and the irrigating measure is a single source. In that case we prove that all branches of optimal irrigation trees satisfy an elliptic equation and that their curvature is a bounded measure. In consequence all branching points in the network have a tangent cone made of a finite number of segments, and all other points have a tangent. An explicit counterexample disproves these regularity properties for non-Lebesgue irrigated measures.en
dc.relation.isversionofjnlnameArchive for Rational Mechanics and Analysis
dc.relation.isversionofjnlvol195en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2010-02
dc.relation.isversionofjnlpages499-531en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00205-008-0210-9en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00360976/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen


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