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| HAL: hal-00262386, version 4 |
| arXiv: 0807.2627 |
| Detailed view |  Export this paper |
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| Interfaces and free boundaries 11, 1 (2009) 153-176 |
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| Available versions: | v1 (2008-03-11) | v2 (2008-04-01) | v3 (2008-07-16) | v4 (2009-03-12) |
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| Level set approach for fractional mean curvature flows |
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| Cyril Imbert 1 |
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| (2009) |
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| This paper is concerned with the study of a geometric flow whose law involves a singular integral operator. This operator is used to define a non-local mean curvature of a set. Moreover the associated flow appears in two important applications: dislocation dynamics and phase field theory for fractional reaction-diffusion equations. It is defined by using the level set method. The main results of this paper are: on one hand, the proper level set formulation of the geometric flow; on the other hand, stability and comparison results for the geometric equation associated with the flow. |
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| 1: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| CEREMADE |
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| Subject | : | Mathematics/Analysis of PDEs |
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| fractional mean curvature – mean curvature – geometric flows – dislocation dynamics – level set approach – stability results – comparison principles – generalized flows |
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| hal-00262386, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00262386 | |
| oai:hal.archives-ouvertes.fr:hal-00262386 | |
| From: Cyril Imbert | |
| Submitted on: Thursday, 12 March 2009 10:35:59 | |
| Updated on: Saturday, 4 April 2009 09:08:25 | |
