On cell problems for Hamilton-Jacobi equations with non-coercive   Hamiltonians and its application to homogenization problems
  We study a cell problem arising in homogenization for a Hamilton-Jacobi equation whose Hamiltonian is not coercive. We introduce a generalized notion of effective Hamiltonians by approximating the equation and characterize the solvability of the cell problem in terms of the generalized effective Hamiltonian. Under some sufficient conditions, the result is applied to the associated homogenization problem. We also show that homogenization for non-coercive equations fails in general. 
Nao Hamamuki, Atsushi Nakayasu, Tokinaga Namba
math.AP