dc.contributor.author Giorgieri, Elena dc.contributor.author Cardaliaguet, Pierre dc.contributor.author Cannarsa, Piermarco dc.date.accessioned 2012-05-30T14:38:54Z dc.date.available 2012-05-30T14:38:54Z dc.date.issued 2007 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/9302 dc.language.iso en en dc.subject Hölder continuous functions en dc.subject viscosity solutions en dc.subject eikonal equation en dc.subject semiconcave functions en dc.subject singularities en dc.subject Normal distance en dc.subject.ddc 515 en dc.title Hölder regularity of the normal distance with an application to a PDE model for growing sandpiles. en dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother Dipartimento di Matematica [Roma II] (DIPMAT) http://www.mat.uniroma2.it/ Universita degli studi di Roma Tor Vergata;Italie dc.description.abstracten Given 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. en dc.relation.isversionofjnlname Transactions of the American Mathematical Society dc.relation.isversionofjnlvol 359 en dc.relation.isversionofjnlissue 6 en dc.relation.isversionofjnldate 2007 dc.relation.isversionofjnlpages 2741-2775 en dc.relation.isversionofdoi http://dx.doi.org/10.1090/S0002-9947-07-04259-6 en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher AMS en dc.subject.ddclabel Analyse en
﻿

Fichiers attachés à cette notice

FichiersTailleFormatConsulter

Il n'y a pas de fichiers associés à cette notice.