Geodesic
Level set approach for fractional mean curvature flows
Cyril Imbert1
1Université Paris-Est Créteil Val de Marne, France
Interfaces and free boundaries, Tome 11 (2009) no. 1, pp. 153-176

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DOI

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 phasefield 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.
DOI : 10.4171/ifb/207
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Fractional mean curvature, mean curvature, geometric flows, dislocation dynamics, level set approach, stability results, comparison principles, generalized flows

Cyril Imbert  1

1 Université Paris-Est Créteil Val de Marne, France 
Cyril Imbert. Level set approach for fractional mean curvature flows. Interfaces and free boundaries, Tome 11 (2009) no. 1, pp. 153-176. doi: 10.4171/ifb/207
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     title = {Level set approach for fractional mean curvature flows},
     journal = {Interfaces and free boundaries},
     pages = {153--176},
     year = {2009},
     volume = {11},
     number = {1},
     doi = {10.4171/ifb/207},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/207/}
}
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