Convergence of the solutions of the discounted equation: the discrete case

被引：16

作者：

Davini, Andrea ^{[1
]}

Fathi, Albert ^{[2
,3
]}

Iturriaga, Renato ^{[4
]}

Zavidovique, Maxime ^{[5
]}

机构：

[1] Sapienza Univ Roma, Dip Matemat, Ple Aldo Moro 2, I-00185 Rome, Italy

[2] ENS Lyon, UMPA, 46 Allee Italie, F-69364 Lyon 7, France

[3] IUF, 46 Allee Italie, F-69364 Lyon 7, France

[4] Cimat, Guanajuato 36000, Mexico

[5] UPMC, IMJ PRG Projet Anal Algebr, 4 Pl Jussieu,Case 247, F-75252 Paris 5, France

来源：

MATHEMATISCHE ZEITSCHRIFT | 2016年 / 284卷 / 3-4期

关键词：

Cost Function; Comparison Principle; Discrete Version; Jacobi Equation; Discrete Case;

D O I：

10.1007/s00209-016-1685-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive a discrete version of the results of Davini et al. (Convergence of the solutions of the discounted Hamilton-Jacobi equation. Invent Math, 2016). If M is a compact metric space, a continuous cost function and , the unique solution to the discrete -discounted equation is the only function such that We prove that there exists a unique constant such that the family of is bounded as and that for this , the family uniformly converges to a function which then verifies The proofs make use of Discrete Weak KAM theory. We also characterize in terms of Peierls barrier and projected Mather measures.

引用

页码：1021 / 1034

页数：14

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