On the Monge–Kantorovich Mass Transfer Problem in Higher Dimensions  

作　　者：Xiao Jun LU 

机构地区：[1]School of Mathematics,Southeast University,Nanjing 210096,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第8期1989-2004,共16页数学学报（英文版）

摘　　要：This paper mainly investigates the approximation of a global maximizer of the Monge–Kantorovich mass transfer problem in higher dimensions through the approach of nonlinear partial differential equations with Dirichlet boundary.Using an approximation mechanism,the primal maximization problem can be transformed into a sequence of minimization problems.By applying the systematic canonical duality theory,one is able to derive a sequence of analytic solutions for the minimization problems.In the final analysis,the convergence of the sequence to an analytical global maximizer of the primal Monge–Kantorovich problem will be demonstrated.

关 键 词：Monge-Kantorovich mass transfer singular variational problem canonical duality theory 

分 类 号：O224[理学—运筹学与控制论]