LIMIT OF THE INFINITE HORIZON DISCOUNTED HAMILTON-JACOBI EQUATION

被引：23

作者：

Iturriaga, Renato ^{[1
]}

Sanchez-Morgado, Hector ^{[2
]}

机构：

[1] CIMAT, Guanajuato 3600, Mexico

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2011年 / 15卷 / 03期

关键词：

Hamilton-Jacobi equation; LAGRANGIAN SYSTEMS; KAM SOLUTIONS; EXISTENCE;

D O I：

10.3934/dcdsb.2011.15.623

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Motivated by the in finite horizon discounted problem, we study the convergence of solutions of the Hamilton Jacobi equation when the discount vanishes. If the Aubry set consists in a finite number of hyperbolic critical points, we give an explicit expression for the limit. Additionaly, we give a new characterization of Mane's critical value as for wich the set of viscosity solutions is equibounded.

引用

页码：623 / 635

页数：13

共 14 条

[1]

Anantharaman N, 2005, DISCRETE CONT DYN-B, V5, P513

[2]

[Anonymous], 1994, MATH APPL

[3]

Bardi M., 1997, Optimal control and viscosity solutions of HamiltonJacobi-Bellman equations

[4] Existence of C1,1 critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds [J].

Bernard, Patrick .

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2007, 40 (03) :445-452

[5] Action potential and weak KAM solutions [J].

Contreras, G .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2001, 13 (04) :427-458

[6]

Contreras G., 1999, 22 COL BRAS MAT I MA

[7] Weak conjugate KAM solutions and Peierls's barriers [J].

Fathi, A .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 325 (06) :649-652

[8] A weak KAM theorem and Mather's theory of Lagrangian systems [J].

Fathi, A .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 324 (09) :1043-1046

[9] On convergence of the Lax-Oleinik semi-group [J].

Fathi, A .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 327 (03) :267-270

[10] Existence of C1 critical subsolutions of the Hamilton-Jacobi equation [J].

Fathi, A ;

Siconolfi, A .

INVENTIONES MATHEMATICAE, 2004, 155 (02) :363-388

← 1 2 →