Characterization of the existence of solutions for Hamilton-Jacobi equations in ergodic control problems with applications

M. Arisawa; H. Ishii; P. L. Lions

doi:10.1007/s002450010001

Characterization of the existence of solutions for Hamilton-Jacobi equations in ergodic control problems with applications

M. Arisawa^*, H. Ishii, P. L. Lions

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	35-50
Number of pages	16
Journal	Applied Mathematics and Optimization
Volume	42
Issue number	1
DOIs	https://doi.org/10.1007/s002450010001
Publication status	Published - 2000 Jul
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1007/s002450010001

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title = "Characterization of the existence of solutions for Hamilton-Jacobi equations in ergodic control problems with applications",

abstract = "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.",

author = "M. Arisawa and H. Ishii and Lions, {P. L.}",

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AU - Ishii, H.

AU - Lions, P. L.

PY - 2000/7

Y1 - 2000/7

N2 - 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.

AB - 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.

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DO - 10.1007/s002450010001

M3 - Article

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Characterization of the existence of solutions for Hamilton-Jacobi equations in ergodic control problems with applications

Abstract

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