Level set approach for fractional mean curvature flows

  • Cyril Imbert

    Université Paris-Est Créteil Val de Marne, France


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.

Cite this article

Cyril Imbert, Level set approach for fractional mean curvature flows. Interfaces Free Bound. 11 (2009), no. 1, pp. 153–176

DOI 10.4171/IFB/207