A short time existence/uniqueness result for a nonlocal topology-preserving segmentation model
Le Guyader, Carole; Forcadel, Nicolas (2012), A short time existence/uniqueness result for a nonlocal topology-preserving segmentation model, Journal of Differential Equations, 253, 3, p. 977-995. http://dx.doi.org/10.1016/j.jde.2012.03.013
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00543911/fr/
Journal nameJournal of Differential Equations
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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.
Subjects / Keywordstopology-preserving segmentation model; viscosity solution theory; partial differential equations; Lipschitz regularity; functional minimization problem
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Penedo, M. G.; Cohen, Laurent D.; Ortega, M.; Barreira, Noellia (2010) Article accepté pour publication ou publié