WEAK SOLUTIONS OF MONGE-AMPIERE TYPE EQUATIONS IN OPTIMAL TRANSPORTATION

This paper concerns the weak solutions of some Monge-Amp~re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere type equations is discussed. A uniform estimate for solution of the Dirichlet problem...

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Bibliographic Details
Published in:数学物理学报：B辑英文版 2013 (4), p.950-962
Main Author: 蒋飞达 杨孝平
Format: Article
Language:English
Subjects:
Dirichlet问题
优化
安培
弱解
方程组
粘性解
边界值
运输
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Summary:This paper concerns the weak solutions of some Monge-Amp~re type equa- tions in the optimal transportation theory. The relationship between the Aleksandrov solutions and the viscosity solutions of the Monge-Ampere type equations is discussed. A uniform estimate for solution of the Dirichlet problem with homogeneous boundary value is obtained.
ISSN:0252-9602
1572-9087