Regularity of Free Boundaries in Anisotropic Capillarity Problems and the Validity of Young’s Law
Regularity of Free Boundaries in Anisotropic Capillarity Problems and the Validity of Young’s Law
复制标题
各向异性毛细管问题中自由边界的规律性和杨氏定律的有效性
DOI：
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发表时间：
2014
影响因子：
2.5
通讯作者：
F. Maggi
中科院分区：
文献类型：
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作者：
G. Philippis;F. Maggi
各向异性毛细问题中的局部体积约束最小化器在其容器壁上形成自由边界。我们证明了可忽略集外的自由边界的正则性，特别是在自由边界的几乎每一点上都证明了杨氏定律的有效性。我们的正则性结果并不特定于毛细问题，实际上适用于有限周长集（因此适用于余维一整数可整流），在其他具有自由边界的变分问题中作为最小化产生。
Local volume-constrained minimizers in anisotropic capillarity problems develop free boundaries on the walls of their containers. We prove the regularity of the free boundary outside a closed negligible set, showing in particular the validity of Young’s law at almost every point of the free boundary. Our regularity results are not specific to capillarity problems, and actually apply to sets of finite perimeter (and thus to codimension one integer rectifiable currents) arising as minimizers in other variational problems with free boundaries.