Dynamics of optimal partial transport

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• 作者：Gonzalo Dávila ; Young-Heon Kim
• 关键词：Mathematics Subject Classification46N10 ; 28A75 ; 35J96 ; 35R35
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：55
• 期：5
• 全文大小：523 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835
• 卷排序：55

文摘

Optimal partial transport, which was initially studied by Caffarelli and McCann (Ann Math (2) 171(2):673–730, 2010), is a variant of optimal transport theory, where only a portion of mass is to be transported in an efficient way. Free boundaries naturally arise as the boundary of the region where the actual transport occurs. This paper considers the evolution dynamics of the free boundaries in terms of the change of m, the allowed amount of transported mass or the change of \(\lambda \), the transportation cost cap, i.e. the allowed maximum cost for a unit mass to be transported. Focusing on the quadratic cost function, we show Hölder and Lipschitz estimates on the speed of the free boundary motion in terms of m and \(\lambda \), respectively. It is also shown that the parameter m is a Lipschitz function of \(\lambda \), which previously was known only to be a continuous increasing function (Caffarelli and McCann Ann Math (2) 171(2):673–730, 2010).