Stable anisotropic capillary hypersurfaces in a wedge
We study a variational problem for hypersurfaces in a wedge in the Euclidean space. Our wedge is bounded by a finitely many hyperplanes passing a common point. The total energy of each hypersurface is the sum of its anisotropic surface energy and the wetting energy of the planar domain bounded by th...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-05-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.202302910.3934/mbe.2022310 |
| _version_ | 1797824667807907840 |
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| author | Miyuki Koiso |
| author_facet | Miyuki Koiso |
| author_sort | Miyuki Koiso |
| collection | DOAJ |
| description | We study a variational problem for hypersurfaces in a wedge in the Euclidean space. Our wedge is bounded by a finitely many hyperplanes passing a common point. The total energy of each hypersurface is the sum of its anisotropic surface energy and the wetting energy of the planar domain bounded by the boundary of the considered hypersurface. An anisotropic surface energy is a generalization of the surface area which was introduced to model the surface tension of a small crystal. We show an existence and uniqueness result of local minimizers of the total energy among hypersurfaces enclosing the same volume. Our result is new even when the special case where the surface energy is the surface area. |
| first_indexed | 2024-03-13T10:42:27Z |
| format | Article |
| id | doaj.art-c8ca53cff8ab4c72a5ba608e5ad64ca8 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-13T10:42:27Z |
| publishDate | 2023-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-c8ca53cff8ab4c72a5ba608e5ad64ca82023-05-18T01:15:27ZengAIMS PressMathematics in Engineering2640-35012023-05-015212210.3934/mine.2023029Stable anisotropic capillary hypersurfaces in a wedgeMiyuki Koiso0Institute of Mathematics for Industry, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, JapanWe study a variational problem for hypersurfaces in a wedge in the Euclidean space. Our wedge is bounded by a finitely many hyperplanes passing a common point. The total energy of each hypersurface is the sum of its anisotropic surface energy and the wetting energy of the planar domain bounded by the boundary of the considered hypersurface. An anisotropic surface energy is a generalization of the surface area which was introduced to model the surface tension of a small crystal. We show an existence and uniqueness result of local minimizers of the total energy among hypersurfaces enclosing the same volume. Our result is new even when the special case where the surface energy is the surface area.https://www.aimspress.com/article/doi/10.3934/mine.202302910.3934/mbe.2022310wulff shapecapillary surfaceanisotropic surface energyconstant anisotropic mean curvaturestablewetting energy |
| spellingShingle | Miyuki Koiso Stable anisotropic capillary hypersurfaces in a wedge Mathematics in Engineering wulff shape capillary surface anisotropic surface energy constant anisotropic mean curvature stable wetting energy |
| title | Stable anisotropic capillary hypersurfaces in a wedge |
| title_full | Stable anisotropic capillary hypersurfaces in a wedge |
| title_fullStr | Stable anisotropic capillary hypersurfaces in a wedge |
| title_full_unstemmed | Stable anisotropic capillary hypersurfaces in a wedge |
| title_short | Stable anisotropic capillary hypersurfaces in a wedge |
| title_sort | stable anisotropic capillary hypersurfaces in a wedge |
| topic | wulff shape capillary surface anisotropic surface energy constant anisotropic mean curvature stable wetting energy |
| url | https://www.aimspress.com/article/doi/10.3934/mine.202302910.3934/mbe.2022310 |
| work_keys_str_mv | AT miyukikoiso stableanisotropiccapillaryhypersurfacesinawedge |