Slow periodic homogenization for Hamilton-Jacobi equations

Capuzzo-Dolcetta and Ishii proved that the rate of periodic homogenization for coercive Hamilton-Jacobi equations is $O({\epsilon }^{1\mathrm{/}3})$. We complement this result by constructing examples of coercive nonconvex Hamiltonians whose rate of periodic homogenization is $\mathrm{\Omega }({\epsilon }^{1\mathrm{/}2})$.