Homogenization of Hamilton-Jacobi equations on domains with small scale periodic structure
Kazuo Horie, Hitoshi Ishii · Indiana University Mathematics Journal · 1998
We study the convergence of solutions of Hamilton-Jacobi equations on domains with small scale periodic structure as the frequency of periodicity tends to infinity.We treat both the Neumann-type and the Dirichlet boundary value problems.The limit functions are characterized as unique solutions of Hamilton-Jacobi equations with the Hamiltonians determined by the corresponding cell problems.