Optimal convergence rates in periodic homogenization of nonconvex Hamilton--Jacobi equations

We study the convergence rates in periodic homogenization of general nonconvex, coercive Hamilton–Jacobi equations. We show that the optimal convergence rate is $O({\epsilon }^{1\mathrm{/}2})$ in one dimension, $O({\epsilon }^{1\mathrm{/}3})$ in two dimensions (up to a logarithmic factor), and $O({\epsilon }^{1\mathrm{/}3})$ in dimension three or higher.