Level set approach for fractional mean curvature flows
Analysis of PDEs
2009-04-04 v2
Abstract
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.
Cite
@article{arxiv.0807.2627,
title = {Level set approach for fractional mean curvature flows},
author = {Cyril Imbert},
journal= {arXiv preprint arXiv:0807.2627},
year = {2009}
}