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<p>We prove that the minimizing movements scheme á 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 Chambolle et al. (Arch Ration Mech Anal 218(3):1263–1329, 2015. 10.1007/s00205-015-0880-z). 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.</p>

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Variational nonlinear and nonlocal curvature flows

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • Daniele De Gennaro

摘要

We prove that the minimizing movements scheme á 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 Chambolle et al. (Arch Ration Mech Anal 218(3):1263–1329, 2015. 10.1007/s00205-015-0880-z). 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.