A characterization of the existence of solutions for Hamilton—Jacobi equations in ergodic control problems with applications

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Date
2000
Indexation documentaire
Analyse
Subject
Hamilton–Jacobi equations; Ergodic control problems; Viscosity solutions; Homogenization; Effective Hamiltonians
Nom de la revue
Applied Mathematics and Optimization
Volume
42
Numéro
1
Date de publication
2000
Pages article
35-50
Nom de l'éditeur
Springer-Verlag
DOI
http://dx.doi.org/10.1007/s002450010001
URI
https://basepub.dauphine.fr/handle/123456789/6501
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Auteur
Ishii, Hitoshi
Lions, Pierre-Louis
Arisawa, Mariko
Type
Article accepté pour publication ou publié
Résumé en anglais
We give a characterization of the existence of bounded solutions for Hamilton–Jacobi equations in ergodic control problems with state-constraint. This result is applied to the reexamination of the counterexample given in [5] concerning the existence of solutions for ergodic control problems in infinite-dimensional Hilbert spaces and also establishing results on effective Hamiltonians in periodic homogenization of Hamilton–Jacobi equations.