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From Hopf--Lax Formula to Optimal Weak Transfer Plan
SIAM Journal on Mathematical Analysis ( IF 2 ) Pub Date : 2020-06-30 , DOI: 10.1137/17m1152231
Yan Shu

SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 3052-3072, January 2020.
We study the properties of the Hopf--Lax formula restricted to convex functions and provide a characterization of the optimal transfer plan for weak transport problems on the real line. On $n$ dimensional real space, we also provide a sufficient condition on the potential function such that the optimal plan of the classical Monge--Kantorovich problem does not depend on the cost function. As a byproduct, we establish a link between the combinatorial object (the permutation polytope) and the Hamilton--Jacobi equation.


中文翻译:

从Hopf-Lax公式到最佳弱转移计划

SIAM数学分析杂志,第52卷,第3期,第3052-3072页,2020年1月。
我们研究了限于凸函数的Hopf-Lax公式的性质,并提供了针对弱运输问题的最优转移计划的特征。实线。在$ n $维实空间上,我们还提供了潜在函数的充分条件,以使经典Monge-Kantorovich问题的最优计划不依赖于成本函数。作为副产品,我们在组合对象(排列多义位)和汉密尔顿-雅各比方程之间建立了联系。
更新日期:2020-06-30
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