Pré-Publication, Document De Travail Année : 2025

Variational Nonlinear and Nonlocal Curvature Flows

Résumé

We prove that the minimizing movements scheme \'a la Almgren-Taylor-Wang converges towards level-set solutions to a nonlinear version of nonlocal curvature flows with time-depending forcing term, in the rather general framework of variational curvatures introduced in \cite{ChaMorPon15}. The nonlinearity involved is assumed to satisfy minimal assumptions, namely continuity, monotonicity, and vanishing at zero. Under additional assumptions only on the curvatures involved, we establish uniqueness for level-set solutions.
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Dates et versions

hal-04520152 , version 1 (25-03-2024)
hal-04520152 , version 2 (31-03-2024)
hal-04520152 , version 3 (10-04-2024)
hal-04520152 , version 4 (23-10-2024)
hal-04520152 , version 5 (10-01-2025)

Identifiants

  • HAL Id : hal-04520152 , version 5

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Daniele de Gennaro. Variational Nonlinear and Nonlocal Curvature Flows. 2025. ⟨hal-04520152v5⟩
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