Slow periodic homogenization for Hamilton-Jacobi equations

Abstract

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