Level set approach for fractional mean curvature flows

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.
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Submitted on : Thursday, March 12, 2009 - 10:35:59 AM
Last modification on : Wednesday, February 19, 2020 - 8:56:26 AM
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  • HAL Id : hal-00262386, version 4
  • ARXIV : 0807.2627

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Cyril Imbert. Level set approach for fractional mean curvature flows. Interfaces and Free Boundaries, European Mathematical Society, 2009, 11 (1), pp.153-176. ⟨hal-00262386v4⟩

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