Minimizing movements for forced anisotropic curvature flow of droplets
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929277893607424 |
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| author | Kholmatov, Shokhrukh Yu. |
| author_facet | Kholmatov, Shokhrukh Yu. |
| contents | We study forced anisotropic curvature flow of droplets on an inhomogeneous horizontal hyperplane. As in [Bellettini, Kholmatov: J. Math. Pures Appl. (2018)] we establish the existence of smooth flow, starting from a regular droplet and satisfying the prescribed anisotropic Young's law, and also the existence of a $1/2$-Hölder continuous in time minimizing movement solution starting from a set of finite perimeter. Furthermore, we investigate various properties of minimizing movements, including comparison principles, uniform boundedness and the consistency with the smooth flow. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_09902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimizing movements for forced anisotropic curvature flow of droplets Kholmatov, Shokhrukh Yu. Analysis of PDEs Differential Geometry 53C44, 49Q20, 35A15, 35D30, 35D35 We study forced anisotropic curvature flow of droplets on an inhomogeneous horizontal hyperplane. As in [Bellettini, Kholmatov: J. Math. Pures Appl. (2018)] we establish the existence of smooth flow, starting from a regular droplet and satisfying the prescribed anisotropic Young's law, and also the existence of a $1/2$-Hölder continuous in time minimizing movement solution starting from a set of finite perimeter. Furthermore, we investigate various properties of minimizing movements, including comparison principles, uniform boundedness and the consistency with the smooth flow. |
| title | Minimizing movements for forced anisotropic curvature flow of droplets |
| topic | Analysis of PDEs Differential Geometry 53C44, 49Q20, 35A15, 35D30, 35D35 |
| url | https://arxiv.org/abs/2403.09902 |