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

Ishii, Hitoshi; Lions, Pierre-Louis; Arisawa, Mariko (2000), A characterization of the existence of solutions for Hamilton—Jacobi equations in ergodic control problems with applications, Applied Mathematics and Optimization, 42, 1, p. 35-50. http://dx.doi.org/10.1007/s002450010001

Type
Article accepté pour publication ou publié
Date
2000
Journal name
Applied Mathematics and Optimization
Volume
42
Number
1
Publisher
Springer-Verlag
Pages
35-50
Publication identifier
Metadata
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Author(s)
Ishii, Hitoshi
Lions, Pierre-Louis
Arisawa, Mariko
Abstract (EN)
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.
Subjects / Keywords
Hamilton–Jacobi equations; Ergodic control problems; Viscosity solutions; Homogenization; Effective Hamiltonians