### Abstract

We consider the homogenization problem for fully nonlinear first order scalar partial differential equations of Hamilton-Jacobi type such as u^{ε}(x) + H (x, x/ε, Du^{ε}(x)) = 0, x ∈ ℝ^{N}, where ε is a small positive parameter and H is a periodic function of the second variable. Our main results (Theorems 1.1 and 1.2 below) give estimates on the rate of convergence of u^{ε} to the solution U of the homogenized problem u(x) + H̄(x, Du(x)) = 0, x ∈ ℝ^{N}.

Original language | English |
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Pages (from-to) | 1113-1128 |

Number of pages | 16 |

Journal | Indiana University Mathematics Journal |

Volume | 50 |

Issue number | 3 |

Publication status | Published - 2001 Sep |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Capuzzo-Dolcetta, I., & Ishii, H. (2001). On the rate of convergence in homogenization of Hamilton-Jacobi equations.

*Indiana University Mathematics Journal*,*50*(3), 1113-1128.