### Abstract

We study the convergence of solutions of Hamilton-Jacobi equations on domains with small scale periodic structure as the frequency of periodicity tends to infinity. We treat both the Neumann-type and the Dirichlet boundary value problems. The limit functions are characterized as unique solutions of Hamilton-Jacobi equations with the Hamiltonians determined by the corresponding cell problems.

Original language | English |
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Pages (from-to) | 1011-1058 |

Number of pages | 48 |

Journal | Indiana University Mathematics Journal |

Volume | 47 |

Issue number | 3 |

Publication status | Published - 1998 Sep |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Horie, K., & Ishii, H. (1998). Homogenization of Hamilton-Jacobi Equations on Domains with Small Scale Periodic Structure.

*Indiana University Mathematics Journal*,*47*(3), 1011-1058.