  We study homogenization for a class of stationnary Hamilton-Jacobi equations
in which the Hamiltonian is obtained by perturbing near the origin an otherwise
periodic Hamiltonian. We prove that the limiting problem consists of a
Hamilton-Jacobi equation outside the origin, with the same effective
Hamiltonian as in periodic homogenization, supplemented at the origin with an
effective Dirichlet condition that keeps track of the perturbation. Various
comments and extensions are discussed.
