Fractional mean curvature flows
Résumé
This paper is concerned with the study of a geometric flow whose law involves a singular integral operator. Such an operator is used to define a non-local mean curvature of a set and for this reason, the flow is referred to as fractional. Such a flow appears in two important applications: dislocation dynamics and phasefield theory for fractional reaction-diffusion equations. It is first defined by using the level-set method. It is proved that it can be also defined in terms of generalized flows (Barles, Souganidis, 1998) so that phasefield theory for fractional reaction-diffusion can be treated (see the working paper of the author and Souganidis).
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