Existence and convergence of the length-preserving elastic flow of clamped curves
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866914854958268416 |
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| author | Rupp, Fabian Spener, Adrian |
| author_facet | Rupp, Fabian Spener, Adrian |
| contents | We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative $L^2$-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long time existence and proving a constrained Lojasiewicz-Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_06991 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Existence and convergence of the length-preserving elastic flow of clamped curves Rupp, Fabian Spener, Adrian Analysis of PDEs Differential Geometry 53E40 (primary), 35K52, 35K55(secondary) We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative $L^2$-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long time existence and proving a constrained Lojasiewicz-Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity. |
| title | Existence and convergence of the length-preserving elastic flow of clamped curves |
| topic | Analysis of PDEs Differential Geometry 53E40 (primary), 35K52, 35K55(secondary) |
| url | https://arxiv.org/abs/2009.06991 |