Stable anisotropic capillary hypersurfaces in a wedge
Stable anisotropic capillary hypersurfaces in a wedge
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DOI：
10.3934/mine.2023029
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发表时间：
2022
影响因子：
1
通讯作者：
Miyuki Koiso
中科院分区：
文献类型：
--
作者：
Miyuki Koiso
研究了欧氏空间中楔形超曲面的一个变分问题。我们的楔由一个过公共点的超平面包围。每个超曲面的总能量是它的各向异性表面能和由所考虑的超曲面的边界限定的平面域的润湿能之和。各向异性表面能是表面积的概括，它被引入来模拟小晶体的表面张力。我们证明了包围相同体积的超曲面之间总能量局部极小值的存在性和唯一性结果。我们的结果是新的，即使在特殊情况下，表面能是表面积。
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.