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dc.contributor.authorLe Guyader, Carole
dc.contributor.authorForcadel, Nicolas
dc.date.accessioned2010-12-13T14:42:25Z
dc.date.available2010-12-13T14:42:25Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/5284
dc.language.isoenen
dc.subjecttopology-preserving segmentation modelen
dc.subjectviscosity solution theoryen
dc.subjectpartial differential equationsen
dc.subjectLipschitz regularityen
dc.subjectfunctional minimization problemen
dc.subject.ddc515en
dc.titleA short time existence/uniqueness result for a nonlocal topology-preserving segmentation modelen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire Mathématique de l'INSA (LMI) Université de Rouen – Institut National des Sciences Appliquées de Rouen;France
dc.description.abstractenMotivated by a prior applied work of Vese and the second author dedicated to segmentation under topological constraints, we derive a slightly modified model phrased as a functional minimization problem, and propose to study it from a theoretical viewpoint. The mathematical model leads to a second order nonlinear PDE with a singularity at $\nabla u=0$ and containing a nonlocal term. A suitable setting is thus the one of the viscosity solution theory and, in this framework, we establish a short time existence/uniqueness result as well as a Lipschitz regularity result for the solution.en
dc.relation.isversionofjnlnameJournal of Differential Equations
dc.relation.isversionofjnlvol253
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpages977-995
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.jde.2012.03.013
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00543911/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelAnalyseen


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