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In this paper, we establish the higher order convergence rates in periodichomogenization of viscous Hamilton-Jacobi equations, which is convex and growsquadratically in the gradient variable. We observe that although the nonlinearstructure governs the first order approximation, the nonlinear effect isabsorbed as an external source term of a linear equation in the second andhigher order approximation. Moreover, we find that the geometric shape of theinitial data has to be chosen carefully according to the effective Hamiltonian,in order to achieve the higher order convergence rates.

Higher Order Convergence Rates in Theory of Homogenization III: viscous Hamilton-Jacobi Equations