Axially symmetric volume constrained anisotropic mean curvature flow

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• 作者：Bennett Palmer (1)
  Wenxiang Zhu (1)
  
• 关键词：Primary 35K55 ; 35K51 ; Secondary 49Q10
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：50
• 期：3-4
• 页码：639-663
• 全文大小：
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• 作者单位：Bennett Palmer (1)
  Wenxiang Zhu (1)
  
  1. Department of Mathematics, Idaho State University, Pocatello, ID, 83209, USA
  
• ISSN：1432-0835

文摘

We study the long time existence theory for a non local flow associated to a free boundary problem for a trapped non liquid drop. The drop has free boundary components on two horizontal plates and its free energy is anisotropic and axially symmetric. For axially symmetric initial surfaces with sufficiently large volume in comparison with their initial surface energy, we show that the flow exists for all time. Numerical simulations of the curvature flow are presented.