A Nonlocal Mean Curvature Flow and Its Semi-implicit Time-Discrete Approximation

DOI10.1137/120863587zbMath1270.35019arXiv1201.5330OpenAlexW1998910501MaRDI QIDQ4907740

Antonin Chambolle, Massimiliano Morini, Marcello Ponsiglione

Publication date: 22 February 2013

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.5330

zbMATH Keywords

minimizing movementsdegenerate Hamiltoniansnonlocal geometric flowsmethod of minimizing movements

Mathematics Subject Classification ID

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Nonlocal diffusion of smooth sets ⋮ Nonlocal curvature flows ⋮ Short time existence of the classical solution to the fractional mean curvature flow ⋮ On the nonlocal curvatures of surfaces with or without boundary ⋮ Isoperimetric problems for a nonlocal perimeter of Minkowski type ⋮ The Cheeger problem in abstract measure spaces ⋮ Neckpinch singularities in fractional mean curvature flows ⋮ Minimizers for nonlocal perimeters of Minkowski type ⋮ Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows ⋮ Decay estimates for evolutionary equations with fractional time-diffusion ⋮ Finite element discretizations of nonlocal minimal graphs: Convergence ⋮ Heteroclinic connections and Dirichlet problems for a nonlocal functional of oscillation type ⋮ Continuity results for TV-minimizers ⋮ A fractional notion of length and an associated nonlocal curvature ⋮ On a Minkowski geometric flow in the plane: Evolution of curves with lack of scale invariance

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