Optimal partial mass transportation and obstacle Monge-Kantorovich equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Igbida, Noureddine¹  Van Thanh Nguyen^1,2 

[1] Univ Limoges, Fac Sci & Tech, UMR CNRS 6172, Inst Rech XLIM DMI, Limoges, France

[2] Quy Nhon Univ, Dept Math, Qui Nhon, Vietnam

关键词: Optimal transport;    Optimal partial transport;    Monge-Kantorovich problem;    Minimum flow problem;    Obstacle Monge-Kantorovich equation;    Nonlinear PDE;   

DOI  :  10.1016/j.jde.2018.01.034

来源: Elsevier

【 摘 要 】

Optimal partial mass transport, which is a variant of the optimal transport problem, consists in transporting effectively a prescribed amount of mass from a source to a target. The problem was first studied by Caffarelli and McCann (2010) [6] and Figalli (2010) [12] with a particular attention to the quadratic cost. Our aim here is to study the optimal partial mass transport problem with Finsler distance costs including the Monge cost given by the Euclidian distance. Our approach is different and our results do not follow from previous works. Among our results, we introduce a PDE of Monge-Kantorovich type with a double obstacle to characterize active submeasures, Kantorovich potential and optimal flow for the optimal partial transport problem. This new PDE enables us to study the uniqueness and monotonicity results for the active submeasures. Another interesting issue of our approach is its convenience for numerical analysis and computations that we develop in a separate paper [14] (Igbida and Nguyen, 2018). (C) 2018 Published by Elsevier Inc.

【 授权许可】

Free