Variational Nonlinear and Nonlocal Curvature Flows
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909641056714752 |
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| author | De Gennaro, Daniele |
| author_facet | De Gennaro, Daniele |
| contents | 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 \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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational Nonlinear and Nonlocal Curvature Flows De Gennaro, Daniele Analysis of PDEs 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 \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. |
| title | Variational Nonlinear and Nonlocal Curvature Flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.05951 |