Level set approach for fractional mean curvature flows

Details Level set approach for fractional mean curvature flows Level set approach for fractional mean curvature flows

2008-07-16

arxiv.org/abs/0807.2627v2

Interfaces and free boundaries 11, 1 (2009) 153-176

Mathematics

Analysis of PDEs

Scientific paper

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.

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