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Hölder regularity of the normal distance with an application to a PDE model for growing sandpiles.

hal.structure.identifierDipartimento di Matematica [Roma II] [DIPMAT]
dc.contributor.authorCannarsa, Piermarco*
hal.structure.identifierDipartimento di Matematica [Roma II] [DIPMAT]
dc.contributor.authorGiorgieri, Elena*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorCardaliaguet, Pierre*
dc.date.accessioned2012-05-30T14:38:54Z
dc.date.available2012-05-30T14:38:54Z
dc.date.issued2007
dc.identifier.issn0002-9947
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/9302
dc.language.isoenen
dc.subjectNormal distance
dc.subjecteikonal equation
dc.subjectsingularities
dc.subjectsemiconcave functions
dc.subjectHölder continuous functions
dc.subjectviscosity solutions
dc.subject.ddc515en
dc.titleHölder regularity of the normal distance with an application to a PDE model for growing sandpiles.
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDipartimento di Matematica [Roma II] (DIPMAT) http://www.mat.uniroma2.it/ Universita degli studi di Roma Tor Vergata;Italie
dc.description.abstractenGiven a bounded domain $ \Omega$ in $ \mathbb{R}^2$ with smooth boundary, the cut locus $ \overline \Sigma$ is the closure of the set of nondifferentiability points of the distance $ d$ from the boundary of $ \Omega$. The normal distance to the cut locus, $ \tau(x)$, is the map which measures the length of the line segment joining $ x$ to the cut locus along the normal direction $ Dd(x)$, whenever $ x\notin \overline \Sigma$. Recent results show that this map, restricted to boundary points, is Lipschitz continuous, as long as the boundary of $ \Omega$ is of class $ C^{2,1}$. Our main result is the global Hölder regularity of $ \tau$ in the case of a domain $ \Omega$ with analytic boundary. We will also show that the regularity obtained is optimal, as soon as the set of the so-called regular conjugate points is nonempty. In all the other cases, Lipschitz continuity can be extended to the whole domain $ \Omega$. The above regularity result for $ \tau$ is also applied to derive the Hölder continuity of the solution of a system of partial differential equations that arises in granular matter theory and optimal mass transfer.
dc.relation.isversionofjnlnameTransactions of the American Mathematical Society
dc.relation.isversionofjnlvol359
dc.relation.isversionofjnlissue6
dc.relation.isversionofjnldate2007
dc.relation.isversionofjnlpages2741-2775
dc.relation.isversionofdoihttp://dx.doi.org/10.1090/S0002-9947-07-04259-6
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherAmerican Mathematical Society
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-10-08T09:36:34Z
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