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

consider the homogenization problem for fully nonlinear first order scalar partial differential equations of Hamilton-Jacobi type such as u(epsilon)(x) + H (x, x/epsilon, Du(epsilon) (x)) = 0, x is an element of R-N, E where epsilon 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 uepsilon to the solution u of the homogenized problem u(x) + (H) over bar (x, Du (x)) = 0, x is an element of R-N.