Some results on anisotropic fractional mean curvature flows

Antonin Chambolle; Matteo Novaga; Berardo Ruffini

doi:10.4171/IFB/387

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$Some results on anisotropic fractional mean curvature flows$

Journal article

Open access

Peer reviewed

Some results on anisotropic fractional mean curvature flows

Antonin Chambolle, Matteo Novaga and Berardo Ruffini

Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications, Vol.19(3)

2017

DOI: https://doi.org/10.4171/IFB/387

Abstract

Fractional curvature

mean curvature flow

diffusion generated motion

convexity

35K93, 53C44, 35R11, 35D40

We show the consistency of a threshold dynamics type algorithm for the anisotropic motion by fractional mean curvature, in the presence of a time dependent forcing term. Beside the consistency result, we show that convex sets remain convex during the evolution, and the evolution of a bounded convex set is uniquely defined.

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Title: Some results on anisotropic fractional mean curvature flows
Creators - without role: Antonin Chambolle - Laboratoire d'Informatique de l'École Polytechnique
Matteo Novaga - Dipartimento di Matematica [Pisa]
Berardo Ruffini - Université de Montpellier, Institut Montpelliérain Alexander Grothendieck - IMAG
Publication Details: Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications, Vol.19(3)
Identifiers: 9935660809311
Academic Unit: Institut Montpelliérain Alexander Grothendieck - IMAG
Language: English
Resource Type: Journal article
Local Fields: hal-01291718