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A short time existence/uniqueness result for a nonlocal topology-preserving segmentation model

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Date
2012
Link to item file
http://hal.archives-ouvertes.fr/hal-00543911/fr/
Dewey
Analyse
Sujet
topology-preserving segmentation model; viscosity solution theory; partial differential equations; Lipschitz regularity; functional minimization problem
Journal issue
Journal of Differential Equations
Volume
253
Number
3
Publication date
2012
Article pages
977-995
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.jde.2012.03.013
URI
https://basepub.dauphine.fr/handle/123456789/5284
Collections
  • CEREMADE : Publications
Metadata
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Author
Le Guyader, Carole
Forcadel, Nicolas
Type
Article accepté pour publication ou publié
Abstract (EN)
Motivated 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.

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