Level set approach for fractional mean curvature flows

Cyril Imbert (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: fractional mean curvature; mean curvature; geometric flows; dislocation dynamics; level set approach; stability results; comparison principles; generalized flows

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert. Level set approach for fractional mean curvature flows. 2008. ⟨hal-00262386v3⟩