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Level set approach for fractional mean curvature flows

Imbert, Cyril (2009), Level set approach for fractional mean curvature flows, Interfaces and free boundaries, 11, 1, p. 153-176

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00262386/en/
Date
2009
Journal name
Interfaces and free boundaries
Volume
11
Number
1
Publisher
European Mathematical Society
Pages
153-176
Metadata
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Author(s)
Imbert, Cyril cc
Abstract (EN)
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.
Subjects / Keywords
fractional mean curvature; generalized flows; comparison principles; stability results; level set approach; dislocation dynamics; geometric flows; mean curvature