Level set approach for fractional mean curvature flows
نویسنده
چکیده
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.
منابع مشابه
Brian White - Mean Curvature Flow (math 258) Lecture Notes Notes by Otis Chodosh
1. Overview 2 1.1. Curve shortening flow 2 1.2. Flow of hypersurfaces 5 1.3. Mean convex surfaces 6 2. The maximum principle 7 3. Unparameterized mean curvature flow 8 3.1. Graphs 8 4. Short-time existence and smoothing 9 5. Long term behavior of mean curvature flow 9 6. Renormalized mean curvature flow 11 7. The level set approach to weak limits 13 8. Weak compactness of submanifolds 16 8.1. E...
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