数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 950-962.doi: 10.1016/S0252-9602(13)60054-5

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WEAK SOLUTIONS OF MONGE-AMPÈRE TYPE EQUATIONS IN OPTIMAL TRANSPORTATION

 蒋飞达, 杨孝平   

  1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
  • 收稿日期:2012-06-15 修回日期:2012-09-15 出版日期:2013-07-20 发布日期:2013-07-20
  • 基金资助:

    This work was supported by National Natural Science Foundation of China (11071119).

WEAK SOLUTIONS OF MONGE-AMPÈRE TYPE EQUATIONS IN OPTIMAL TRANSPORTATION

 |Jiang Fei-Da, YANG Xiao-Ping   

  1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
  • Received:2012-06-15 Revised:2012-09-15 Online:2013-07-20 Published:2013-07-20
  • Supported by:

    This work was supported by National Natural Science Foundation of China (11071119).

摘要:

This paper concerns the weak solutions of some Monge-Amp`ere type equa-tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Amp`ere type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.

关键词: viscosity solution, generalized solution, optimal transportation equation

Abstract:

This paper concerns the weak solutions of some Monge-Amp`ere type equa-tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Amp`ere type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.

Key words: viscosity solution, generalized solution, optimal transportation equation

中图分类号: 

  • 35J60