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

We consider the homogenization problem for fully nonlinear first order scalar partial differential equations of Hamilton-Jacobi type such as u(x) + H ( x, x ! , Du(x) ) = 0, x ∈ R , where ! 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! to the solution u of the homogenized problem u(x) + H(x,Du(x)) = 0, x ∈ R . ∗Partially supported by EC-TMR Network ERBFMRCT980234 ”Viscosity Solutions and Applications” †Supported in part by the Grant-In-Aid for Scientific Research, No. 09440067, the JSPS, Japan.