### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Indiana University Mathematics Journal*,

*50*(3), 1113-1128.

**On the rate of convergence in homogenization of Hamilton-Jacobi equations.** / Capuzzo-Dolcetta, I.; Ishii, H.

Research output: Contribution to journal › Article

*Indiana University Mathematics Journal*, vol. 50, no. 3, pp. 1113-1128.

}

TY - JOUR

T1 - On the rate of convergence in homogenization of Hamilton-Jacobi equations

AU - Capuzzo-Dolcetta, I.

AU - Ishii, H.

PY - 2001/9

Y1 - 2001/9

N2 - We consider the homogenization problem for fully nonlinear first order scalar partial differential equations of Hamilton-Jacobi type such as uε(x) + H (x, x/ε, Duε(x)) = 0, x ∈ ℝN, 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 uε to the solution U of the homogenized problem u(x) + H̄(x, Du(x)) = 0, x ∈ ℝN.

AB - We consider the homogenization problem for fully nonlinear first order scalar partial differential equations of Hamilton-Jacobi type such as uε(x) + H (x, x/ε, Duε(x)) = 0, x ∈ ℝN, 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 uε to the solution U of the homogenized problem u(x) + H̄(x, Du(x)) = 0, x ∈ ℝN.

UR - http://www.scopus.com/inward/record.url?scp=0039300006&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039300006&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0039300006

VL - 50

SP - 1113

EP - 1128

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 3

ER -